From 77012ea20e4025a9b04dbf23a538fa5a9b5cb082 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 1 Jul 2019 00:54:53 -0400
Subject: [PATCH 01/35] sketch the boiler plate for bnaf

---
 numpyro/contrib/nn/bna_nn.py          | 48 +++++++++++++++++++++++++++
 numpyro/distributions/distribution.py |  4 ---
 numpyro/distributions/flows.py        | 25 ++++++++++++++
 3 files changed, 73 insertions(+), 4 deletions(-)
 create mode 100644 numpyro/contrib/nn/bna_nn.py
 create mode 100644 numpyro/distributions/flows.py

diff --git a/numpyro/contrib/nn/bna_nn.py b/numpyro/contrib/nn/bna_nn.py
new file mode 100644
index 000000000..48e777d6a
--- /dev/null
+++ b/numpyro/contrib/nn/bna_nn.py
@@ -0,0 +1,48 @@
+def MaskedBlockDense():
+    def init_fun(rng, input_shape):
+        return output_shape, params
+
+    def apply_fun(params, inputs, **kwargs):
+        x, logdet = inputs
+        # TODO: implement
+        return o, logdet
+
+
+def Tanh():
+    def init_fun(rng, input_shape):
+        return 
+
+    def apply_fun(params, inputs, **kwargs):
+        x, logdet = inputs
+        return o, logdet
+
+
+def stax_serial_with_jacobian(*layers):
+    """
+    Works like `stax.serial` but also forward the log determinant of Jacobian.
+    """
+    nlayers = len(layers)
+    init_funs, apply_funs = zip(*layers)
+
+    def init_fun(rng, input_shape):
+        params = []
+        for init_fun in init_funs:
+          rng, layer_rng = random.split(rng)
+          input_shape, param = init_fun(layer_rng, input_shape)
+          params.append(param)
+        return input_shape, params
+
+    def apply_fun(params, inputs, **kwargs):
+        rng = kwargs.pop('rng', None)
+        rngs = random.split(rng, nlayers) if rng is not None else (None,) * nlayers
+        for fun, param, rng in zip(apply_funs, params, rngs):
+          inputs = fun(param, inputs, rng=rng, **kwargs)
+        return inputs
+
+    return init_fun, apply_fun
+
+
+def BlockNeuralAutoregressiveNN(input_dim, hidden_factor):
+    # TODO: support multi hidden factors
+    layers = [MaskedBlockDense(hidden_factor), Tanh(), MaskedBlockDense(input_dim)]
+    return stax_serial_with_jacobian(*layers)
diff --git a/numpyro/distributions/distribution.py b/numpyro/distributions/distribution.py
index 4a7648314..383333a28 100644
--- a/numpyro/distributions/distribution.py
+++ b/numpyro/distributions/distribution.py
@@ -185,10 +185,6 @@ def support(self):
             domain = t.codomain
         return domain
 
-    @property
-    def is_reparametrized(self):
-        return self.base_dist.reparametrized
-
     def sample(self, key, sample_shape=()):
         x = self.base_dist.sample(key, sample_shape)
         for transform in self.transforms:
diff --git a/numpyro/distributions/flows.py b/numpyro/distributions/flows.py
new file mode 100644
index 000000000..4ffd1b0c7
--- /dev/null
+++ b/numpyro/distributions/flows.py
@@ -0,0 +1,25 @@
+class BlockNeuralAutoregressiveTransform(Transform):
+    event_dim = 1
+
+    def __init__(self, bna_nn, params):
+        self.bna_nn = bna_nn
+        self.params = params
+
+    def __call__(self, x):
+        self._cached_x = x
+        y, self._cached_logdet = self.bna_nn(self.params, x)
+        return y
+
+    def inv(self, y, caching=True):
+        if caching:
+            return self._cached_x
+        else:
+            raise ValueError("Block neural autoregressive transform does not have an analytic"
+                             " inverse implemented.")
+
+    def log_abs_det_jacobian(self, x, y, caching=True):
+        if caching:
+            return self._cached_logdet
+        else:
+            _, logdet = self.bna_nn(self.params, x)
+            return logdet

From b4f2a82c3c50f86023e988bf748a7fd17a32f108 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 1 Jul 2019 09:25:12 -0400
Subject: [PATCH 02/35] add permute and nn.Tanh

---
 numpyro/contrib/nn/bna_nn.py         |  9 +++++++--
 numpyro/distributions/constraints.py | 21 +++++++++++++++++++++
 numpyro/distributions/util.py        |  4 ++++
 3 files changed, 32 insertions(+), 2 deletions(-)

diff --git a/numpyro/contrib/nn/bna_nn.py b/numpyro/contrib/nn/bna_nn.py
index 48e777d6a..81e9650a8 100644
--- a/numpyro/contrib/nn/bna_nn.py
+++ b/numpyro/contrib/nn/bna_nn.py
@@ -1,3 +1,6 @@
+from numpyro.distributions.util import softplus
+
+
 def MaskedBlockDense():
     def init_fun(rng, input_shape):
         return output_shape, params
@@ -10,11 +13,13 @@ def apply_fun(params, inputs, **kwargs):
 
 def Tanh():
     def init_fun(rng, input_shape):
-        return 
+        return input_shape, ()
 
     def apply_fun(params, inputs, **kwargs):
         x, logdet = inputs
-        return o, logdet
+        y = np.tanh(x)
+        tanh_logdet = - 2 * (x - np.log(2.) + softplus(-2 * x))
+        return y, logdet + tanh_logdet  # TODO: reshape?
 
 
 def stax_serial_with_jacobian(*layers):
diff --git a/numpyro/distributions/constraints.py b/numpyro/distributions/constraints.py
index 92f606e78..c5294e405 100644
--- a/numpyro/distributions/constraints.py
+++ b/numpyro/distributions/constraints.py
@@ -25,6 +25,7 @@
 import math
 
 import jax.numpy as np
+from jax import ops
 from jax.scipy.special import expit, logit
 
 from numpyro.distributions.util import (
@@ -384,6 +385,26 @@ def log_abs_det_jacobian(self, x, y):
         return x[..., -n:].sum(-1)
 
 
+class PermuteTransfrom(torch.nn.Module):
+    event_dim = 1
+
+    def __init__(self, permutation):
+        self.permutation = permutation
+
+    def __call__(self, x):
+        return x[..., self.permutation]
+
+    def inv(self, y):
+        size = self.permutation.size
+        permutation_inv = ops.index_update(np.zeros(size, dtype=np.int64),
+                                           np.arange(size),
+                                           np.arange(size))
+        return x[..., permutation_inv]
+
+    def log_abs_det_jacobian(self, x, y):
+        return np.full(np.shape(x)[:-1], 0.)
+
+
 class PowerTransform(Transform):
     domain = positive
     codomain = positive
diff --git a/numpyro/distributions/util.py b/numpyro/distributions/util.py
index a621a6a6d..48e822ff0 100644
--- a/numpyro/distributions/util.py
+++ b/numpyro/distributions/util.py
@@ -462,6 +462,10 @@ def signed_stick_breaking_tril(t):
     return y
 
 
+def softplus(x):
+    return np.logaddexp(x, 0.)
+
+
 # The is sourced from: torch.distributions.util.py
 #
 # Copyright (c) 2016-     Facebook, Inc            (Adam Paszke)

From 871d55e2a6378eff88d7f8739e80caf4481c05b4 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 8 Jul 2019 14:10:24 -0400
Subject: [PATCH 03/35] tries to find valid init_params

---
 numpyro/hmc_util.py | 31 ++++++++++++++++++++++++++-----
 1 file changed, 26 insertions(+), 5 deletions(-)

diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index 068c896a0..a2998f78d 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -1,7 +1,7 @@
 from collections import namedtuple
 
 import jax
-from jax import grad, jit, partial, random, value_and_grad, vmap
+from jax import device_get, grad, jit, partial, random, value_and_grad, vmap
 from jax.flatten_util import ravel_pytree
 import jax.numpy as np
 from jax.ops import index_update
@@ -775,9 +775,30 @@ def single_chain_init(key, only_params=False):
                     potential_energy(seeded_model, model_args, model_kwargs, inv_transforms),
                     jax.partial(transform_fn, inv_transforms))
 
+    _, potential_fn, constrain_fn = single_chain_init(rng if rng.ndim == 1 else rng[0])
+
+    def single_chain_init_validated(key):
+        def cond_fn(state):
+            i, _, params = state
+            z = ravel_pytree(params)[0]
+            z_grad = ravel_pytree(grad(potential_fn)(params))[0]
+            return ~((i < 100) & np.all(np.isfinite(z)) & np.all(np.isfinite(z_grad)))
+
+        def body_fn(state):
+            i, key, _ = state
+            key, subkey = random.split(key)
+            params = single_chain_init(subkey, only_params=True)
+            return i + 1, key, params
+
+        init_params = single_chain_init(key, only_params=True)
+        num_tries, _, init_params = while_loop(cond_fn, body_fn, (0, key, init_params))
+        return init_params, num_tries
+
     if rng.ndim == 1:
-        return single_chain_init(rng)
+        init_params, num_tries = single_chain_init_validated(rng)
     else:
-        _, potential_fn, constrain_fun = single_chain_init(rng[0])
-        init_params = vmap(lambda rng: single_chain_init(rng, only_params=True))(rng)
-        return init_params, potential_fn, constrain_fun
+        init_params, num_tries = vmap(single_chain_init_validated)(rng)
+
+    if device_get(np.max(num_tries)) == 100:
+        raise RuntimeError("Cannot find valid initial parameters. Please check your model again.")
+    return init_params, potential_fn, constrain_fn

From 98d0315381b5bcf5d327b0d8fd62540ff94d7575 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 10 Jul 2019 19:01:18 -0400
Subject: [PATCH 04/35] move find valid initial params to infer.util

---
 numpyro/contrib/autoguide/__init__.py |  1 +
 numpyro/hmc_util.py                   | 88 ++++++---------------------
 numpyro/infer_util.py                 | 83 ++++++++++++++++++++++++-
 3 files changed, 103 insertions(+), 69 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 16a890ab0..7d7fe968d 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -132,6 +132,7 @@ class AutoContinuous(AutoGuide):
     def __init__(self, rng, model, get_params_fn, prefix="auto", init_loc_fn=init_to_median):
         # Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
         # Use `block` to not record sample primitives in `init_loc_fn`.
+        # TODO: make sure that rng is not reused
         model = substitute(model, substitute_fn=block(seed(init_loc_fn, rng)))
         super(AutoContinuous, self).__init__(model, get_params_fn, prefix=prefix)
 
diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index a2998f78d..e070650bf 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -11,7 +11,7 @@
 from numpyro.distributions.constraints import biject_to, real
 from numpyro.distributions.util import cholesky_inverse
 from numpyro.handlers import seed, trace
-from numpyro.infer_util import log_density, transform_fn
+from numpyro.infer_util import find_valid_initial_params, potential_energy, transform_fn
 from numpyro.util import cond, while_loop
 
 AdaptWindow = namedtuple('AdaptWindow', ['start', 'end'])
@@ -704,20 +704,6 @@ def euclidean_kinetic_energy(inverse_mass_matrix, r):
     return 0.5 * np.dot(v, r)
 
 
-def potential_energy(model, model_args, model_kwargs, inv_transforms):
-    def _potential_energy(params):
-        params_constrained = transform_fn(inv_transforms, params)
-        log_joint, model_trace = log_density(model, model_args, model_kwargs, params_constrained)
-        for name, t in inv_transforms.items():
-            t_log_det = np.sum(t.log_abs_det_jacobian(params[name], params_constrained[name]))
-            if 'scale' in model_trace[name]:
-                t_log_det = model_trace[name]['scale'] * t_log_det
-            log_joint = log_joint + t_log_det
-        return - log_joint
-
-    return _potential_energy
-
-
 def initialize_model(rng, model, *model_args, init_strategy='uniform', **model_kwargs):
     """
     Given a model with Pyro primitives, returns a function which, given
@@ -744,61 +730,27 @@ def initialize_model(rng, model, *model_args, init_strategy='uniform', **model_k
         to convert unconstrained HMC samples to constrained values that
         lie within the site's support.
     """
-    def single_chain_init(key, only_params=False):
-        seeded_model = seed(model, key)
-        model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
-        constrained_values, inv_transforms = {}, {}
-        for k, v in model_trace.items():
-            if v['type'] == 'sample' and not v['is_observed']:
-                constrained_values[k] = v['value']
-                inv_transforms[k] = biject_to(v['fn'].support)
-            elif v['type'] == 'param':
-                constrained_values[k] = v['value']
-                constraint = v['kwargs'].pop('constraint', real)
-                inv_transforms[k] = biject_to(constraint)
-        prior_params = transform_fn(inv_transforms,
-                                    {k: v for k, v in constrained_values.items()}, invert=True)
-        if init_strategy == 'uniform':
-            init_params = {}
-            for k, v in prior_params.items():
-                key, = random.split(key, 1)
-                init_params[k] = random.uniform(key, shape=np.shape(v), minval=-2, maxval=2)
-        elif init_strategy == 'prior':
-            init_params = prior_params
-        else:
-            raise ValueError('initialize={} is not a valid initialization strategy.'.format(init_strategy))
-
-        if only_params:
-            return init_params
-        else:
-            return (init_params,
-                    potential_energy(seeded_model, model_args, model_kwargs, inv_transforms),
-                    jax.partial(transform_fn, inv_transforms))
-
-    _, potential_fn, constrain_fn = single_chain_init(rng if rng.ndim == 1 else rng[0])
-
-    def single_chain_init_validated(key):
-        def cond_fn(state):
-            i, _, params = state
-            z = ravel_pytree(params)[0]
-            z_grad = ravel_pytree(grad(potential_fn)(params))[0]
-            return ~((i < 100) & np.all(np.isfinite(z)) & np.all(np.isfinite(z_grad)))
-
-        def body_fn(state):
-            i, key, _ = state
-            key, subkey = random.split(key)
-            params = single_chain_init(subkey, only_params=True)
-            return i + 1, key, params
-
-        init_params = single_chain_init(key, only_params=True)
-        num_tries, _, init_params = while_loop(cond_fn, body_fn, (0, key, init_params))
-        return init_params, num_tries
+    def single_chain_init(key):
+        return find_valid_initial_params(key, model, *model_args, init_strategy=init_strategy,
+                                         **model_kwargs)
+
+    seeded_model = seed(model, rng if rng.ndim == 1 else rng[0])
+    model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
+    inv_transforms = {}
+    for k, v in model_trace.items():
+        if v['type'] == 'sample' and not v['is_observed']:
+            inv_transforms[k] = biject_to(v['fn'].support)
+        elif v['type'] == 'param':
+            constraint = v['kwargs'].pop('constraint', real)
+            inv_transforms[k] = biject_to(constraint)
+
+    potential_fn = potential_energy(seeded_model, model_args, model_kwargs, inv_transforms)
 
     if rng.ndim == 1:
-        init_params, num_tries = single_chain_init_validated(rng)
+        init_params, is_valid = single_chain_init(rng)
     else:
-        init_params, num_tries = vmap(single_chain_init_validated)(rng)
+        init_params, is_valid = vmap(single_chain_init)(rng)
 
-    if device_get(np.max(num_tries)) == 100:
+    if device_get(~np.all(is_valid)):
         raise RuntimeError("Cannot find valid initial parameters. Please check your model again.")
-    return init_params, potential_fn, constrain_fn
+    return init_params, potential_fn, jax.partial(transform_fn, inv_transforms)
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index 8a3b3a218..ea829d995 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -1,6 +1,10 @@
+from jax import grad, random
+from jax.flatten_util import ravel_pytree
 import jax.numpy as np
 
-from numpyro.handlers import substitute, trace
+from numpyro.distributions.constraints import biject_to, real
+from numpyro.handlers import seed, substitute, trace
+from numpyro.util import while_loop
 
 
 def log_density(model, model_args, model_kwargs, params):
@@ -39,3 +43,80 @@ def transform_fn(transforms, params, invert=False):
     """
     return {k: transforms[k](v) if not invert else transforms[k].inv(v)
             for k, v in params.items()}
+
+
+def potential_energy(model, model_args, model_kwargs, inv_transforms):
+    def _potential_energy(params):
+        params_constrained = transform_fn(inv_transforms, params)
+        log_joint, model_trace = log_density(model, model_args, model_kwargs, params_constrained)
+        for name, t in inv_transforms.items():
+            t_log_det = np.sum(t.log_abs_det_jacobian(params[name], params_constrained[name]))
+            if 'scale' in model_trace[name]:
+                t_log_det = model_trace[name]['scale'] * t_log_det
+            log_joint = log_joint + t_log_det
+        return - log_joint
+
+    return _potential_energy
+
+
+def find_valid_initial_params(rng, model, *model_args, init_strategy='uniform', **model_kwargs):
+    """
+    Given a model with Pyro primitives, returns an initial valid unconstrained
+    parameters. This function also returns an `is_valid` flag to say whether the
+    initial parameters are valid.
+
+    :param jax.random.PRNGKey rng: random number generator seed to
+        sample from the prior. The returned `init_params` will have the
+        batch shape ``rng.shape[:-1]``.
+    :param model: Python callable containing Pyro primitives.
+    :param `*model_args`: args provided to the model.
+    :param str init_strategy: initialization strategy - `uniform`
+        initializes the unconstrained parameters by drawing from
+        a `Uniform(-2, 2)` distribution (as used by Stan), whereas
+        `prior` initializes the parameters by sampling from the prior
+        for each of the sample sites.
+    :param `**model_kwargs`: kwargs provided to the model.
+    :return: tuple of (`init_params`, `is_valid`).
+    """
+    def cond_fn(state):
+        i, _, _, is_valid = state
+        return (i < 100) & (~is_valid)
+
+    def body_fn(state):
+        i, key, _, _ = state
+        key, subkey = random.split(key)
+        # TODO: incorporate init_to_median here
+        seeded_model = seed(model, subkey)
+        model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
+        constrained_values, inv_transforms = {}, {}
+        for k, v in model_trace.items():
+            if v['type'] == 'sample' and not v['is_observed']:
+                constrained_values[k] = v['value']
+                inv_transforms[k] = biject_to(v['fn'].support)
+            elif v['type'] == 'param':
+                constrained_values[k] = v['value']
+                constraint = v['kwargs'].pop('constraint', real)
+                inv_transforms[k] = biject_to(constraint)
+        prior_params = transform_fn(inv_transforms,
+                                    {k: v for k, v in constrained_values.items()}, invert=True)
+        if init_strategy == 'uniform':
+            params = {}
+            for k, v in prior_params.items():
+                key, = random.split(key, 1)
+                params[k] = random.uniform(key, shape=np.shape(v), minval=-2, maxval=2)
+        elif init_strategy == 'prior':
+            params = prior_params
+        else:
+            raise ValueError('initialize={} is not a valid initialization strategy.'.format(init_strategy))
+
+        potential_fn = potential_energy(seeded_model, model_args, model_kwargs, inv_transforms)
+        param_grads = grad(potential_fn)(params)
+        z = ravel_pytree(params)[0]
+        z_grad = ravel_pytree(param_grads)[0]
+        is_valid = np.all(np.isfinite(z)) & np.all(np.isfinite(z_grad))
+        return i + 1, key, params, is_valid
+
+    # NB: the logic here is kind of do-while instead of while-do
+    init_state = body_fn((0, rng, None, None))
+    _, _, init_params, is_valid = while_loop(cond_fn, body_fn, init_state)
+    return init_params, is_valid

From 52867047bf0781b8e32c627f0d685392319171de Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 10 Jul 2019 19:27:17 -0400
Subject: [PATCH 05/35] fix import

---
 test/test_handlers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/test_handlers.py b/test/test_handlers.py
index 5380e18dc..5d903c9c1 100644
--- a/test/test_handlers.py
+++ b/test/test_handlers.py
@@ -4,7 +4,7 @@
 
 import numpyro.distributions as dist
 from numpyro.handlers import sample, scale
-from numpyro.hmc_util import log_density
+from numpyro.infer_util import log_density
 
 
 def test_scale():

From cf059b9be612fd56506625513d5a4dd0aee826ab Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 10 Jul 2019 23:32:02 -0400
Subject: [PATCH 06/35] incorporate various init strategy

---
 numpyro/contrib/autoguide/__init__.py |  1 -
 numpyro/hmc_util.py                   | 10 ++---
 numpyro/infer_util.py                 | 64 ++++++++++++++++++---------
 3 files changed, 45 insertions(+), 30 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 7d7fe968d..16a890ab0 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -132,7 +132,6 @@ class AutoContinuous(AutoGuide):
     def __init__(self, rng, model, get_params_fn, prefix="auto", init_loc_fn=init_to_median):
         # Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
         # Use `block` to not record sample primitives in `init_loc_fn`.
-        # TODO: make sure that rng is not reused
         model = substitute(model, substitute_fn=block(seed(init_loc_fn, rng)))
         super(AutoContinuous, self).__init__(model, get_params_fn, prefix=prefix)
 
diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index e070650bf..aa0e474db 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -11,7 +11,7 @@
 from numpyro.distributions.constraints import biject_to, real
 from numpyro.distributions.util import cholesky_inverse
 from numpyro.handlers import seed, trace
-from numpyro.infer_util import find_valid_initial_params, potential_energy, transform_fn
+from numpyro.infer_util import find_valid_initial_params, init_to_uniform, potential_energy, transform_fn
 from numpyro.util import cond, while_loop
 
 AdaptWindow = namedtuple('AdaptWindow', ['start', 'end'])
@@ -704,7 +704,7 @@ def euclidean_kinetic_energy(inverse_mass_matrix, r):
     return 0.5 * np.dot(v, r)
 
 
-def initialize_model(rng, model, *model_args, init_strategy='uniform', **model_kwargs):
+def initialize_model(rng, model, *model_args, init_strategy=init_to_uniform, **model_kwargs):
     """
     Given a model with Pyro primitives, returns a function which, given
     unconstrained parameters, evaluates the potential energy (negative
@@ -718,11 +718,7 @@ def initialize_model(rng, model, *model_args, init_strategy='uniform', **model_k
         batch shape ``rng.shape[:-1]``.
     :param model: Python callable containing Pyro primitives.
     :param `*model_args`: args provided to the model.
-    :param str init_strategy: initialization strategy - `uniform`
-        initializes the unconstrained parameters by drawing from
-        a `Uniform(-2, 2)` distribution (as used by Stan), whereas
-        `prior` initializes the parameters by sampling from the prior
-        for each of the sample sites.
+    :param callable init_strategy: a per-site initialization function.
     :param `**model_kwargs`: kwargs provided to the model.
     :return: tuple of (`init_params`, `potential_fn`, `constrain_fn`),
         `init_params` are values from the prior used to initiate MCMC,
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index ea829d995..6f6a157d6 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -1,9 +1,12 @@
+from functools import partial
+
 from jax import grad, random
 from jax.flatten_util import ravel_pytree
 import jax.numpy as np
 
+import numpyro.distributions as dist
 from numpyro.distributions.constraints import biject_to, real
-from numpyro.handlers import seed, substitute, trace
+from numpyro.handlers import block, sample, seed, substitute, trace
 from numpyro.util import while_loop
 
 
@@ -59,7 +62,37 @@ def _potential_energy(params):
     return _potential_energy
 
 
-def find_valid_initial_params(rng, model, *model_args, init_strategy='uniform', **model_kwargs):
+def init_to_uniform(site, radius=2):
+    """
+    Initialize to an arbitrary feasible point, ignoring distribution
+    parameters.
+    """
+    if site['is_observed']:
+        return None
+    value = sample('_init', site['fn'])
+    t = biject_to(site['fn'].support)
+    unconstrained_value = sample('_unconstrained_init', dist.Uniform(-radius, radius),
+                                 sample_shape=np.shape(t.inv(value)))
+    return t(unconstrained_value)
+
+
+def init_to_median(site, num_samples=15):
+    """
+    Initialize to the prior median.
+    """
+    if site['is_observed']:
+        return None
+    samples = sample('_init', site['fn'], sample_shape=(num_samples,))
+    value = np.quantile(samples, 0.5, axis=0)
+    return value
+
+
+init_to_feasible = lambda site: init_to_uniform(site, radius=0)
+init_to_prior = lambda site: init_to_median(site, num_samples=1)
+
+
+def find_valid_initial_params(rng, model, *model_args, init_strategy=init_to_uniform,
+                              **model_kwargs):
     """
     Given a model with Pyro primitives, returns an initial valid unconstrained
     parameters. This function also returns an `is_valid` flag to say whether the
@@ -70,11 +103,7 @@ def find_valid_initial_params(rng, model, *model_args, init_strategy='uniform',
         batch shape ``rng.shape[:-1]``.
     :param model: Python callable containing Pyro primitives.
     :param `*model_args`: args provided to the model.
-    :param str init_strategy: initialization strategy - `uniform`
-        initializes the unconstrained parameters by drawing from
-        a `Uniform(-2, 2)` distribution (as used by Stan), whereas
-        `prior` initializes the parameters by sampling from the prior
-        for each of the sample sites.
+    :param callable init_strategy: a per-site initialization function.
     :param `**model_kwargs`: kwargs provided to the model.
     :return: tuple of (`init_params`, `is_valid`).
     """
@@ -85,8 +114,8 @@ def cond_fn(state):
     def body_fn(state):
         i, key, _, _ = state
         key, subkey = random.split(key)
-        # TODO: incorporate init_to_median here
-        seeded_model = seed(model, subkey)
+
+        seeded_model = substitute(model, substitute_fn=block(seed(init_strategy, subkey)))
         model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
         constrained_values, inv_transforms = {}, {}
         for k, v in model_trace.items():
@@ -97,19 +126,10 @@ def body_fn(state):
                 constrained_values[k] = v['value']
                 constraint = v['kwargs'].pop('constraint', real)
                 inv_transforms[k] = biject_to(constraint)
-        prior_params = transform_fn(inv_transforms,
-                                    {k: v for k, v in constrained_values.items()}, invert=True)
-        if init_strategy == 'uniform':
-            params = {}
-            for k, v in prior_params.items():
-                key, = random.split(key, 1)
-                params[k] = random.uniform(key, shape=np.shape(v), minval=-2, maxval=2)
-        elif init_strategy == 'prior':
-            params = prior_params
-        else:
-            raise ValueError('initialize={} is not a valid initialization strategy.'.format(init_strategy))
-
-        potential_fn = potential_energy(seeded_model, model_args, model_kwargs, inv_transforms)
+        params = transform_fn(inv_transforms,
+                              {k: v for k, v in constrained_values.items()}, invert=True)
+
+        potential_fn = potential_energy(model, model_args, model_kwargs, inv_transforms)
         param_grads = grad(potential_fn)(params)
         z = ravel_pytree(params)[0]
         z_grad = ravel_pytree(param_grads)[0]

From 4443f1329f2bd570c177a6a480776979ff2588e7 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Thu, 11 Jul 2019 21:50:20 -0400
Subject: [PATCH 07/35] use init strategy in autoguide

---
 numpyro/contrib/autoguide/__init__.py | 66 ++++++---------------------
 numpyro/hmc_util.py                   |  2 +-
 numpyro/infer_util.py                 | 45 ++++++++++++------
 test/test_hmc_util.py                 | 22 ++++++++-
 4 files changed, 68 insertions(+), 67 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 16a890ab0..6e51393e5 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -1,7 +1,6 @@
 # Adapted from pyro.contrib.autoguide
 from abc import ABC, abstractmethod
 
-import numpy as onp
 import scipy.stats as osp
 
 from jax import vmap
@@ -12,49 +11,16 @@
 from numpyro.distributions import constraints
 from numpyro.distributions.constraints import biject_to
 from numpyro.distributions.util import sum_rightmost
-from numpyro.handlers import block, param, sample, seed, substitute, trace
-from numpyro.infer_util import transform_fn
+from numpyro.handlers import block, param, sample, seed, trace
+from numpyro.infer_util import find_valid_initial_params, init_to_median, transform_fn
 
 __all__ = [
     'AutoContinuous',
     'AutoGuide',
     'AutoDiagonalNormal',
-    'init_to_feasible',
-    'init_to_median',
 ]
 
 
-def init_to_feasible(site):
-    """
-    Initialize to an arbitrary feasible point, ignoring distribution
-    parameters.
-    """
-    if site['is_observed']:
-        return None
-    value = sample('_init', site['fn'])
-    t = biject_to(site['fn'].support)
-    return t(np.zeros(np.shape(t.inv(value))))
-
-
-def init_to_median(site, num_samples=15):
-    """
-    Initialize to the prior median; fallback to a feasible point if median is
-    undefined.
-    """
-    if site['is_observed']:
-        return None
-    try:
-        # Try to compute empirical median.
-        samples = sample('_init', site['fn'], sample_shape=(num_samples,))
-        value = onp.median(samples, axis=0)
-        if np.isnan(value):
-            raise ValueError
-        return value
-    except ValueError:
-        # Fall back to feasible point.
-        return init_to_feasible(site)
-
-
 class AutoGuide(ABC):
     """
     Base class for automatic guides.
@@ -126,32 +92,30 @@ class AutoContinuous(AutoGuide):
         Blei
 
     :param callable model: A Pyro model.
-    :param callable init_loc_fn: A per-site initialization function.
+    :param callable init_strategy: A per-site initialization function.
         See :ref:`autoguide-initialization` section for available functions.
     """
-    def __init__(self, rng, model, get_params_fn, prefix="auto", init_loc_fn=init_to_median):
-        # Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
-        # Use `block` to not record sample primitives in `init_loc_fn`.
-        model = substitute(model, substitute_fn=block(seed(init_loc_fn, rng)))
+    def __init__(self, rng, model, get_params_fn, prefix="auto", init_strategy=init_to_median):
+        self.rng = rng
+        self.init_strategy = init_strategy
+        model = seed(model, rng)
         super(AutoContinuous, self).__init__(model, get_params_fn, prefix=prefix)
 
     def _setup_prototype(self, *args, **kwargs):
         super(AutoContinuous, self)._setup_prototype(*args, **kwargs)
+        # FIXME: without block statement, get AssertionError: all sites must have unique names
+        init_params, is_valid = block(find_valid_initial_params)(self.rng, self.model, *args,
+                                                                 init_strategy=self.init_strategy,
+                                                                 **kwargs)
         self._inv_transforms = {}
-        unconstrained_sites = {}
         for name, site in self.prototype_trace.items():
             if site['type'] == 'sample' and not site['is_observed']:
-                # Collect the shapes of unconstrained values.
-                # These may differ from the shapes of constrained values.
-                transform = biject_to(site['fn'].support)
-                unconstrained_val = transform.inv(site['value'])
-                self._inv_transforms[name] = transform
-                unconstrained_sites[name] = unconstrained_val
-
-        latent_size = sum(np.size(x) for x in unconstrained_sites.values())
+                self._inv_transforms[name] = biject_to(site['fn'].support)
+
+        latent_size = sum(np.size(x) for x in init_params.values())
         if latent_size == 0:
             raise RuntimeError('{} found no latent variables; Use an empty guide instead'.format(type(self).__name__))
-        self._init_latent, self._unravel_fn = ravel_pytree(unconstrained_sites)
+        self._init_latent, self._unravel_fn = ravel_pytree(init_params)
 
     def __call__(self, *args, **kwargs):
         """
diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index aa0e474db..54f695c91 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -728,7 +728,7 @@ def initialize_model(rng, model, *model_args, init_strategy=init_to_uniform, **m
     """
     def single_chain_init(key):
         return find_valid_initial_params(key, model, *model_args, init_strategy=init_strategy,
-                                         **model_kwargs)
+                                         param_as_improper=True, **model_kwargs)
 
     seeded_model = seed(model, rng if rng.ndim == 1 else rng[0])
     model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index 6f6a157d6..b0d0b4722 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -1,5 +1,3 @@
-from functools import partial
-
 from jax import grad, random
 from jax.flatten_util import ravel_pytree
 import jax.numpy as np
@@ -62,6 +60,26 @@ def _potential_energy(params):
     return _potential_energy
 
 
+def init_to_median(site, num_samples=15):
+    """
+    Initialize to the prior median.
+    """
+    if site['is_observed']:
+        return None
+    samples = sample('_init', site['fn'], sample_shape=(num_samples,))
+    value = np.quantile(samples, 0.5, axis=0)
+    return value
+
+
+def init_to_prior(site):
+    """
+    Initialize to a prior sample.
+    """
+    if site['is_observed']:
+        return None
+    return sample('_init', site['fn'])
+
+
 def init_to_uniform(site, radius=2):
     """
     Initialize to an arbitrary feasible point, ignoring distribution
@@ -76,23 +94,20 @@ def init_to_uniform(site, radius=2):
     return t(unconstrained_value)
 
 
-def init_to_median(site, num_samples=15):
+def init_to_feasible(site):
     """
-    Initialize to the prior median.
+    Initialize to an arbitrary feasible point, ignoring distribution
+    parameters.
     """
     if site['is_observed']:
         return None
-    samples = sample('_init', site['fn'], sample_shape=(num_samples,))
-    value = np.quantile(samples, 0.5, axis=0)
-    return value
-
-
-init_to_feasible = lambda site: init_to_uniform(site, radius=0)
-init_to_prior = lambda site: init_to_median(site, num_samples=1)
+    value = sample('_init', site['fn'])
+    t = biject_to(site['fn'].support)
+    return t(np.zeros(np.shape(t.inv(value))))
 
 
 def find_valid_initial_params(rng, model, *model_args, init_strategy=init_to_uniform,
-                              **model_kwargs):
+                              param_as_improper=False, **model_kwargs):
     """
     Given a model with Pyro primitives, returns an initial valid unconstrained
     parameters. This function also returns an `is_valid` flag to say whether the
@@ -104,6 +119,8 @@ def find_valid_initial_params(rng, model, *model_args, init_strategy=init_to_uni
     :param model: Python callable containing Pyro primitives.
     :param `*model_args`: args provided to the model.
     :param callable init_strategy: a per-site initialization function.
+    :param bool param_as_improper: a flag to decide whether to consider sites with
+        `param` statement as sites with improper priors.
     :param `**model_kwargs`: kwargs provided to the model.
     :return: tuple of (`init_params`, `is_valid`).
     """
@@ -115,6 +132,8 @@ def body_fn(state):
         i, key, _, _ = state
         key, subkey = random.split(key)
 
+        # Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
+        # Use `block` to not record sample primitives in `init_loc_fn`.
         seeded_model = substitute(model, substitute_fn=block(seed(init_strategy, subkey)))
         model_trace = trace(seeded_model).get_trace(*model_args, **model_kwargs)
         constrained_values, inv_transforms = {}, {}
@@ -122,7 +141,7 @@ def body_fn(state):
             if v['type'] == 'sample' and not v['is_observed']:
                 constrained_values[k] = v['value']
                 inv_transforms[k] = biject_to(v['fn'].support)
-            elif v['type'] == 'param':
+            elif v['type'] == 'param' and param_as_improper:
                 constrained_values[k] = v['value']
                 constraint = v['kwargs'].pop('constraint', real)
                 inv_transforms[k] = biject_to(constraint)
diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index 8ec16cfc8..351c83259 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -23,6 +23,12 @@
     warmup_adapter,
     welford_covariance
 )
+from numpyro.infer_util import (
+    init_to_prior,
+    init_to_uniform,
+    init_to_median,
+    init_to_feasible,
+)
 from numpyro.util import control_flow_prims_disabled, fori_loop, optional
 
 logger = logging.getLogger(__name__)
@@ -387,7 +393,13 @@ def fn(vv_state):
         assert tree.num_proposals > 10
 
 
-@pytest.mark.parametrize('init_strategy', ['prior', 'uniform'])
+@pytest.mark.parametrize('init_strategy', [
+    init_to_feasible,
+    pytest.param(init_to_median,
+                 marks=pytest.mark.xfail(reason="batching rule for quantile not implemented")),
+    init_to_prior,
+    init_to_uniform,
+])
 def test_initialize_model_change_point(init_strategy):
     def model(data):
         alpha = 1 / np.mean(data)
@@ -417,7 +429,13 @@ def model(data):
             assert_allclose(p[i], init_params_i[name], atol=1e-6)
 
 
-@pytest.mark.parametrize('init_strategy', ['prior', 'uniform'])
+@pytest.mark.parametrize('init_strategy', [
+    init_to_feasible,
+    pytest.param(init_to_median,
+                 marks=pytest.mark.xfail(reason="batching rule for quantile not implemented")),
+    init_to_prior,
+    init_to_uniform,
+])
 def test_initialize_model_dirichlet_categorical(init_strategy):
     def model(data):
         concentration = np.array([1.0, 1.0, 1.0])

From 3d23e7e1b0c3c01874d41a606f920a1fd028bd99 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Thu, 1 Aug 2019 11:09:39 -0400
Subject: [PATCH 08/35] use np.mean inplace of np.median

---
 examples/neutra.py                    |  3 +--
 numpyro/contrib/autoguide/__init__.py | 38 +++++++++++----------------
 numpyro/infer_util.py                 |  3 ++-
 test/test_hmc_util.py                 | 10 +++----
 4 files changed, 21 insertions(+), 33 deletions(-)

diff --git a/examples/neutra.py b/examples/neutra.py
index 482ca4694..164cc9f49 100644
--- a/examples/neutra.py
+++ b/examples/neutra.py
@@ -89,8 +89,7 @@ def body_fn(val):
     transformed_potential_fn = make_transformed_pe(potential_fn, transform, unpack_fn)
     transformed_constrain_fn = lambda x: constrain_fn(unpack_fn(transform(x)))  # noqa: E731
 
-    # TODO: expose latent_size in autoguide
-    init_params = np.zeros(np.size(guide._init_latent))
+    init_params = np.zeros(guide.latent_size)
     print("\nStart NeuTra HMC...")
     zs = mcmc(args.num_warmup, args.num_samples, init_params, potential_fn=transformed_potential_fn)
     print("Transform samples into unwarped space...")
diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 8b9624cff..b4832cd1e 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -124,19 +124,15 @@ def _setup_prototype(self, *args, **kwargs):
                                                                  init_strategy=self.init_strategy,
                                                                  **kwargs)
         self._inv_transforms = {}
-        unconstrained_sites = {}
         for name, site in self.prototype_trace.items():
             if site['type'] == 'sample' and not site['is_observed']:
                 # TODO: handle dynamic support
-                transform = biject_to(site['fn'].support)
-                unconstrained_val = transform.inv(site['value'])
-                self._inv_transforms[name] = transform
-                unconstrained_sites[name] = unconstrained_val
+                self._inv_transforms[name] = biject_to(site['fn'].support)
 
-        latent_size = sum(np.size(x) for x in unconstrained_sites.values())
-        if latent_size == 0:
-            raise RuntimeError('{} found no latent variables; Use an empty guide instead'.format(type(self).__name__))
         self._init_latent, self._unravel_fn = ravel_pytree(init_params)
+        self.latent_size = np.size(self._init_latent)
+        if self.latent_size == 0:
+            raise RuntimeError('{} found no latent variables; Use an empty guide instead'.format(type(self).__name__))
 
     @abstractmethod
     def _get_transform(self):
@@ -162,9 +158,8 @@ def __call__(self, *args, **kwargs):
             sample_latent_fn = substitute(sample_latent_fn, params)
 
         base_dist = kwargs.pop('base_dist', None)
-        latent_size = np.size(self._init_latent)
         if base_dist is None:
-            base_dist = _Normal(np.zeros(latent_size), 1.)
+            base_dist = _Normal(np.zeros(self.latent_size), 1.)
         latent = sample_latent_fn(base_dist, *args, **kwargs)
 
         # unpack continuous latent samples
@@ -198,9 +193,8 @@ def get_transform(self, opt_state):
     def sample_posterior(self, rng, opt_state, *args, **kwargs):
         sample_shape = kwargs.pop('sample_shape', ())
         base_dist = kwargs.pop('base_dist', None)
-        latent_size = np.size(self._init_latent)
         if base_dist is None:
-            base_dist = _Normal(np.zeros(latent_size), 1.)
+            base_dist = _Normal(np.zeros(self.latent_size), 1.)
         params = self.get_params(opt_state)
         latent_sample = substitute(seed(self._sample_latent, rng), params)(base_dist, sample_shape=sample_shape)
         return self.unpack_latent(latent_sample)
@@ -230,7 +224,7 @@ def setup(self, *args, **kwargs):
         super(AutoDiagonalNormal, self).setup(*args, **kwargs)
         return {
             '{}_loc'.format(self.prefix): self._init_latent,
-            '{}_scale'.format(self.prefix): np.ones(np.size(self._init_latent)),
+            '{}_scale'.format(self.prefix): np.ones(self.latent_size),
         }
 
     def median(self, opt_state):
@@ -300,44 +294,42 @@ class AutoIAFNormal(AutoContinuous):
     :param int num_flows: the number of flows to be used, defaults to 3.
     :param `**arn_kwargs`: keywords for constructing autoregressive neural networks.
     """
-    def __init__(self, rng, model, get_params_fn, prefix="auto", init_loc_fn=init_to_median,
+    def __init__(self, rng, model, get_params_fn, prefix="auto", init_strategy=init_to_median,
                  num_flows=3, **arn_kwargs):
         self.arn_kwargs = arn_kwargs
         self.arns = []
         self.num_flows = num_flows
         rng, *self.arn_rngs = random.split(rng, num_flows + 1)
         super(AutoIAFNormal, self).__init__(rng, model, get_params_fn, prefix=prefix,
-                                            init_loc_fn=init_loc_fn)
+                                            init_strategy=init_strategy)
 
     def setup(self, *args, **kwargs):
         super(AutoIAFNormal, self).setup(*args, **kwargs)
-        latent_size = np.size(self._init_latent)
-        if latent_size == 1:
+        if self.latent_size == 1:
             raise ValueError('latent dim = 1. Consider using AutoDiagonalNormal instead')
         params = {}
         if not self.arns:
             # 2-layer by default following the experiments in IAF paper
             # (https://arxiv.org/abs/1606.04934) and Neutra paper (https://arxiv.org/abs/1903.03704)
-            hidden_dims = self.arn_kwargs.get('hidden_dims', [latent_size, latent_size])
+            hidden_dims = self.arn_kwargs.get('hidden_dims', [self.latent_size, self.latent_size])
             skip_connections = self.arn_kwargs.get('skip_connections', True)
             nonlinearity = self.arn_kwargs.get('nonlinearity', stax.Relu)
 
             for i in range(self.num_flows):
-                arn_init, arn = AutoregressiveNN(latent_size, hidden_dims,
-                                                 permutation=np.arange(latent_size),
+                arn_init, arn = AutoregressiveNN(self.latent_size, hidden_dims,
+                                                 permutation=np.arange(self.latent_size),
                                                  skip_connections=skip_connections,
                                                  nonlinearity=nonlinearity)
-                _, init_params = arn_init(self.arn_rngs[i], (latent_size,))
+                _, init_params = arn_init(self.arn_rngs[i], (self.latent_size,))
                 params['{}_arn__{}'.format(self.prefix, i)] = init_params
                 self.arns.append(arn)
         return params
 
     def _get_transform(self):
-        latent_size = np.size(self._init_latent)
         flows = []
         for i in range(self.num_flows):
             arn_params = param('{}_arn__{}'.format(self.prefix, i), None)
             if i > 0:
-                flows.append(PermuteTransform(np.arange(latent_size)[::-1]))
+                flows.append(PermuteTransform(np.arange(self.latent_size)[::-1]))
             flows.append(InverseAutoregressiveTransform(self.arns[i], arn_params))
         return ComposeTransform(flows)
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index ffb54d228..2eb173aeb 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -85,7 +85,8 @@ def init_to_median(site, num_samples=15):
     if site['is_observed']:
         return None
     samples = sample('_init', site['fn'], sample_shape=(num_samples,))
-    value = np.quantile(samples, 0.5, axis=0)
+    # TODO: use np.median when it is available upstream
+    value = np.mean(samples, axis=0)
     return value
 
 
diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index c9cc95eca..13cfa3de6 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -14,7 +14,6 @@
 from numpyro.handlers import sample, seed
 from numpyro.hmc_util import (
     AdaptWindow,
-    _cov,
     _is_iterative_turning,
     _leaf_idx_to_ckpt_idxs,
     build_adaptation_schedule,
@@ -429,8 +428,7 @@ def model():
 
 @pytest.mark.parametrize('init_strategy', [
     init_to_feasible,
-    pytest.param(init_to_median,
-                 marks=pytest.mark.xfail(reason="batching rule for quantile not implemented")),
+    init_to_median,
     init_to_prior,
     init_to_uniform,
 ])
@@ -465,8 +463,7 @@ def model(data):
 
 @pytest.mark.parametrize('init_strategy', [
     init_to_feasible,
-    pytest.param(init_to_median,
-                 marks=pytest.mark.xfail(reason="batching rule for quantile not implemented")),
+    init_to_median,
     init_to_prior,
     init_to_uniform,
 ])
@@ -511,8 +508,7 @@ def test_gaussian_subposterior(method, diagonal):
     if diagonal:
         assert_allclose(np.var(draws, axis=0), np.diag(cov), atol=0.05)
     else:
-        # TODO: use np.cov for the next JAX version
-        assert_allclose(_cov(draws), cov, atol=0.05)
+        assert_allclose(np.cov(draws), cov, atol=0.05)
 
 
 @pytest.mark.parametrize('method', [consensus, parametric_draws])

From 3a211bd97b0e7e2aa1270d8ece401fe1f9625a34 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Fri, 2 Aug 2019 11:41:34 -0400
Subject: [PATCH 09/35] dynamic support for svi and autoguide

---
 numpyro/contrib/autoguide/__init__.py | 23 +++++++++++-------
 numpyro/handlers.py                   |  2 ++
 numpyro/infer_util.py                 |  5 +---
 numpyro/svi.py                        | 34 ++++++++++++++++++---------
 4 files changed, 41 insertions(+), 23 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index d26ae6878..964db4c68 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -157,11 +157,14 @@ def _setup_prototype(self, *args, **kwargs):
         unconstrained_sites = {}
         for name, site in self.prototype_trace.items():
             if site['type'] == 'sample' and not site['is_observed']:
-                # TODO: handle dynamic support
-                transform = biject_to(site['fn'].support)
-                unconstrained_val = transform.inv(site['value'])
-                self._inv_transforms[name] = transform
-                unconstrained_sites[name] = unconstrained_val
+                if site['intermediates']:
+                    transform = biject_to(site['fn'].base_dist.support)
+                    self.inv_transforms[name] = transform
+                    unconstrained_sites[name] = transform.inv(site['intermediates'][0][0])
+                else:
+                    transform = biject_to(site['fn'].support)
+                    self.inv_transforms[name] = transform
+                    unconstrained_sites[name] = transform.inv(site['value'])
 
         latent_size = sum(np.size(x) for x in unconstrained_sites.values())
         if latent_size == 0:
@@ -205,9 +208,13 @@ def __call__(self, *args, **kwargs):
             site = self.prototype_trace[name]
             value = transform(unconstrained_value)
             log_density = - transform.log_abs_det_jacobian(unconstrained_value, value)
-            log_density = sum_rightmost(log_density, np.ndim(log_density) - np.ndim(value) +
-                                        len(site['fn'].event_shape))
-            delta_dist = dist.Delta(value, log_density=log_density, event_ndim=len(site['fn'].event_shape))
+            if site['intermediates']:
+                event_ndim = len(site['fn'].base_dist.event_shape)
+            else:
+                event_ndim = len(site['fn'].event_shape)
+            log_density = sum_rightmost(log_density,
+                                        np.ndim(log_density) - np.ndim(value) + event_ndim)
+            delta_dist = dist.Delta(value, log_density=log_density, event_ndim=event_ndim)
             result[name] = sample(name, delta_dist)
 
         return result
diff --git a/numpyro/handlers.py b/numpyro/handlers.py
index 5c12969a3..4ce4931e1 100644
--- a/numpyro/handlers.py
+++ b/numpyro/handlers.py
@@ -196,6 +196,8 @@ def __init__(self, fn, guide_trace):
     def process_message(self, msg):
         if msg['name'] in self.guide_trace:
             msg['value'] = self.guide_trace[msg['name']]['value']
+            if msg['type'] == 'sample':
+                msg['intermediates'] = self.guide_trace[msg['name']]['intermediates']
 
 
 class block(Messenger):
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index a8b5c3a64..bd1bf8367 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -17,10 +17,7 @@ def log_density(model, model_args, model_kwargs, params, skip_dist_transforms=Fa
         domain.
     :return: log of joint density and a corresponding model trace
     """
-    if skip_dist_transforms:
-        model = substitute(model, base_param_map=params)
-    else:
-        model = substitute(model, params)
+    model = substitute(model, base_param_map=params)
     model_trace = trace(model).get_trace(*model_args, **model_kwargs)
     log_joint = 0.
     for site in model_trace.values():
diff --git a/numpyro/svi.py b/numpyro/svi.py
index 30bfee8f9..826af5acd 100644
--- a/numpyro/svi.py
+++ b/numpyro/svi.py
@@ -3,10 +3,11 @@
 import jax
 from jax import random, value_and_grad
 
+from numpyro.contrib.autoguide import AutoContinuous
 from numpyro.distributions import constraints
-from numpyro.distributions.constraints import biject_to
-from numpyro.handlers import replay, seed, substitute, trace
-from numpyro.infer_util import log_density
+from numpyro.distributions.constraints import biject_to, ComposeTransform
+from numpyro.handlers import replay, seed, substitute, trace, Messenger
+from numpyro.infer_util import log_density, transform_fn
 
 
 def _seed(model, guide, rng):
@@ -63,18 +64,21 @@ def init_fn(rng, model_args=(), guide_args=(), params=None):
         guide_trace = trace(guide_init).get_trace(*guide_args, **kwargs)
         model_trace = trace(model_init).get_trace(*model_args, **kwargs)
         inv_transforms = {}
-        for site in list(guide_trace.values()) + list(model_trace.values()):
+        # NB: params in model_trace will be overwritten by params in guide_trace
+        for site in list(model_trace.values()) + list(guide_trace.values()):
             if site['type'] == 'param':
                 constraint = site['kwargs'].pop('constraint', constraints.real)
                 transform = biject_to(constraint)
-                inv_transforms[site['name']] = transform
-                params[site['name']] = transform.inv(site['value'])
-
-        def transform_constrained(inv_transforms, params):
-            return {k: inv_transforms[k](v) for k, v in params.items()}
+                if isinstance(transform, ComposeTransform):
+                    base_transform = transform.parts[0]
+                    inv_transforms[site['name']] = base_transform
+                    params[site['name']] = base_transform(transform.inv(site['value']))
+                else:
+                    inv_transforms[site['name']] = transform
+                    params[site['name']] = site['value']
 
         nonlocal constrain_fn
-        constrain_fn = jax.partial(transform_constrained, inv_transforms)
+        constrain_fn = jax.partial(transform_fn, inv_transforms)
         return optim_init(params), constrain_fn
 
     def update_fn(i, rng, opt_state, model_args=(), guide_args=()):
@@ -151,7 +155,15 @@ def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn):
     """
     param_map = constrain_fn(param_map)
     guide_log_density, guide_trace = log_density(guide, guide_args, kwargs, param_map)
-    model_log_density, _ = log_density(replay(model, guide_trace), model_args, kwargs, param_map)
+    # NB: we only want to substitute params not available in guide_trace
+    param_map = {k: v for k, v in param_map if k not in guide_trace}
+    # NB: only skip transforms for AutoContinuous guide
+    skip_dist_transforms = False
+    guide_fn = guide.fn if isinstance(guide, Messenger) else guide
+    if isinstance(guide_fn, AutoContinuous):
+        skip_dist_transforms = True
+    model_log_density, _ = log_density(replay(model, guide_trace), model_args, kwargs, param_map,
+                                       skip_dist_transforms=skip_dist_transforms)
     # log p(z) - log q(z)
     elbo = model_log_density - guide_log_density
     # Return (-elbo) since by convention we do gradient descent on a loss and

From 6e956ee1e584d2082bfc55df84f57b78a740f4cb Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sat, 3 Aug 2019 12:10:09 -0400
Subject: [PATCH 10/35] fig typos

---
 numpyro/contrib/autoguide/__init__.py |  4 ++--
 numpyro/hmc_util.py                   |  4 ++--
 numpyro/svi.py                        |  2 +-
 test/test_hmc_util.py                 | 13 ++++++++-----
 4 files changed, 13 insertions(+), 10 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 964db4c68..8356cde67 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -159,11 +159,11 @@ def _setup_prototype(self, *args, **kwargs):
             if site['type'] == 'sample' and not site['is_observed']:
                 if site['intermediates']:
                     transform = biject_to(site['fn'].base_dist.support)
-                    self.inv_transforms[name] = transform
+                    self._inv_transforms[name] = transform
                     unconstrained_sites[name] = transform.inv(site['intermediates'][0][0])
                 else:
                     transform = biject_to(site['fn'].support)
-                    self.inv_transforms[name] = transform
+                    self._inv_transforms[name] = transform
                     unconstrained_sites[name] = transform.inv(site['value'])
 
         latent_size = sum(np.size(x) for x in unconstrained_sites.values())
diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index f9940a225..ddc853f23 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -711,11 +711,11 @@ def euclidean_kinetic_energy(inverse_mass_matrix, r):
     return 0.5 * np.dot(v, r)
 
 
-def potential_energy(model, model_args, model_kwargs, inv_transforms, skip_dist_transforms=True):
+def potential_energy(model, model_args, model_kwargs, inv_transforms):
     def _potential_energy(params):
         params_constrained = transform_fn(inv_transforms, params)
         log_joint, model_trace = log_density(model, model_args, model_kwargs, params_constrained,
-                                             skip_dist_transforms=skip_dist_transforms)
+                                             skip_dist_transforms=True)
         for name, t in inv_transforms.items():
             t_log_det = np.sum(t.log_abs_det_jacobian(params[name], params_constrained[name]))
             if 'scale' in model_trace[name]:
diff --git a/numpyro/svi.py b/numpyro/svi.py
index 826af5acd..913c62389 100644
--- a/numpyro/svi.py
+++ b/numpyro/svi.py
@@ -156,7 +156,7 @@ def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn):
     param_map = constrain_fn(param_map)
     guide_log_density, guide_trace = log_density(guide, guide_args, kwargs, param_map)
     # NB: we only want to substitute params not available in guide_trace
-    param_map = {k: v for k, v in param_map if k not in guide_trace}
+    param_map = {k: v for k, v in param_map.items() if k not in guide_trace}
     # NB: only skip transforms for AutoContinuous guide
     skip_dist_transforms = False
     guide_fn = guide.fn if isinstance(guide, Messenger) else guide
diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index 878708375..864529749 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -407,18 +407,21 @@ def model():
     model = seed(model, random.PRNGKey(0))
     inv_transforms = {'x': biject_to(x_prior.support), 'y': biject_to(y_prior.support)}
     expected_samples = partial(transform_fn, inv_transforms)(params)
-    expected_log_density = potential_energy(
-        model, (), {}, inv_transforms, skip_dist_transforms=False)(params)
+    expected_potential_energy = (
+        - x_prior.log_prob(expected_samples['x']) -
+        y_prior.log_prob(expected_samples['y']) -
+        inv_transforms['x'].log_abs_det_jacobian(params['x'], expected_samples['x']) -
+        inv_transforms['y'].log_abs_det_jacobian(params['y'], expected_samples['y'])
+    )
 
     base_inv_transforms = {'x': biject_to(x_prior.support), 'y': biject_to(y_prior.base_dist.support)}
     actual_samples = make_constrain_fn(
         seed(model, random.PRNGKey(0)), (), {}, base_inv_transforms)(params)
-    actual_log_density = potential_energy(
-        model, (), {}, base_inv_transforms, skip_dist_transforms=True)(params)
+    actual_potential_energy = potential_energy(model, (), {}, base_inv_transforms)(params)
 
     assert_allclose(expected_samples['x'], actual_samples['x'])
     assert_allclose(expected_samples['y'], actual_samples['y'])
-    assert_allclose(expected_log_density, actual_log_density)
+    assert_allclose(expected_potential_energy, actual_potential_energy)
 
 
 @pytest.mark.parametrize('init_strategy', ['prior', 'uniform'])

From 818b0623884254e12209ecce3ffb12f6f6f6426d Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sun, 4 Aug 2019 23:17:34 -0400
Subject: [PATCH 11/35] add tests and update autoguide for dynamic support

---
 examples/vae.py                       |  2 +-
 numpyro/contrib/autoguide/__init__.py | 71 ++++++++++++++++-----------
 numpyro/distributions/continuous.py   |  3 ++
 numpyro/hmc_util.py                   | 20 ++------
 numpyro/infer_util.py                 |  7 +++
 numpyro/svi.py                        | 23 ++++++++-
 test/contrib/test_autoguide.py        | 28 +++++++++++
 test/test_svi.py                      | 31 +++++++++++-
 8 files changed, 138 insertions(+), 47 deletions(-)

diff --git a/examples/vae.py b/examples/vae.py
index 780fbd896..9c4db6363 100644
--- a/examples/vae.py
+++ b/examples/vae.py
@@ -16,7 +16,7 @@
 
 
 def sigmoid(x):
-    return 1 / (1 + np.exp(x))
+    return 1 / (1 + np.exp(-x))
 
 
 # TODO: move to JAX
diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index 8356cde67..5a70e7988 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -2,7 +2,6 @@
 from abc import ABC, abstractmethod
 
 import numpy as onp
-import scipy.stats as osp
 
 from jax import random, vmap
 from jax.experimental import stax
@@ -17,7 +16,7 @@
 from numpyro.distributions.flows import InverseAutoregressiveTransform
 from numpyro.distributions.util import sum_rightmost
 from numpyro.handlers import block, param, sample, seed, substitute, trace
-from numpyro.infer_util import transform_fn
+from numpyro.infer_util import constrain_fn, transform_fn
 
 __all__ = [
     'AutoContinuous',
@@ -121,6 +120,8 @@ def _sample_latent(self, *args, **kwargs):
     def _setup_prototype(self, *args, **kwargs):
         # run the model so we can inspect its structure
         self.prototype_trace = block(trace(self.model).get_trace)(*args, **kwargs)
+        self._args = args
+        self._kwargs = kwargs
 
 
 class AutoContinuous(AutoGuide):
@@ -148,12 +149,16 @@ class AutoContinuous(AutoGuide):
     def __init__(self, rng, model, get_params_fn, prefix="auto", init_loc_fn=init_to_median):
         # Wrap model in a `substitute` handler to initialize from `init_loc_fn`.
         # Use `block` to not record sample primitives in `init_loc_fn`.
-        model = substitute(model, substitute_fn=block(seed(init_loc_fn, rng)))
+        # TODO: remove init_loc_fn mechanism in favor of init_strategy
+        # which is addressed in https://github.com/pyro-ppl/numpyro/pull/237
+        # model = substitute(model, substitute_fn=block(seed(init_loc_fn, rng)))
+        model = seed(model, rng)
         super(AutoContinuous, self).__init__(model, get_params_fn, prefix=prefix)
 
     def _setup_prototype(self, *args, **kwargs):
         super(AutoContinuous, self)._setup_prototype(*args, **kwargs)
         self._inv_transforms = {}
+        self._has_transformed_dist = False
         unconstrained_sites = {}
         for name, site in self.prototype_trace.items():
             if site['type'] == 'sample' and not site['is_observed']:
@@ -161,6 +166,7 @@ def _setup_prototype(self, *args, **kwargs):
                     transform = biject_to(site['fn'].base_dist.support)
                     self._inv_transforms[name] = transform
                     unconstrained_sites[name] = transform.inv(site['intermediates'][0][0])
+                    self._has_transformed_dist = True
                 else:
                     transform = biject_to(site['fn'].support)
                     self._inv_transforms[name] = transform
@@ -169,7 +175,7 @@ def _setup_prototype(self, *args, **kwargs):
         latent_size = sum(np.size(x) for x in unconstrained_sites.values())
         if latent_size == 0:
             raise RuntimeError('{} found no latent variables; Use an empty guide instead'.format(type(self).__name__))
-        self._init_latent, self._unravel_fn = ravel_pytree(unconstrained_sites)
+        self._init_latent, self.unpack_latent = ravel_pytree(unconstrained_sites)
 
     @abstractmethod
     def _get_transform(self):
@@ -203,7 +209,7 @@ def __call__(self, *args, **kwargs):
         # unpack continuous latent samples
         result = {}
 
-        for name, unconstrained_value in self._unravel_fn(latent).items():
+        for name, unconstrained_value in self.unpack_latent(latent).items():
             transform = self._inv_transforms[name]
             site = self.prototype_trace[name]
             value = transform(unconstrained_value)
@@ -219,28 +225,39 @@ def __call__(self, *args, **kwargs):
 
         return result
 
-    def unpack_latent(self, latent_sample, transform=True):
+    def _unpack_and_transform(self, latent_sample, params, model_args=None, model_kwargs=None):
         sample_shape = np.shape(latent_sample)[:-1]
         latent_sample = np.reshape(latent_sample, (-1, np.shape(latent_sample)[-1]))
-        unpacked_samples = vmap(self._unravel_fn)(latent_sample)
+        model_args = self._args if model_args is None else model_args
+        model_kwargs = self._kwargs if model_kwargs is None else model_kwargs
+
+        def unpack_single_latent(latent):
+            unpacked_samples = self.unpack_latent(latent)
+            if self._has_transformed_dist:
+                base_param_map = {**params, **unpacked_samples}
+                return constrain_fn(self.model, model_args, model_kwargs,
+                                    self._inv_transforms, base_param_map)
+            else:
+                return transform_fn(self._inv_transforms, unpacked_samples)
+
+        unpacked_samples = vmap(unpack_single_latent)(latent_sample)
         unpacked_samples = tree_map(lambda x: np.reshape(x, sample_shape + np.shape(x)[1:]),
                                     unpacked_samples)
-
-        transform = self._inv_transforms if transform else {}
-        return transform_fn(transform, unpacked_samples)
+        return unpacked_samples
 
     def get_transform(self, opt_state):
         return substitute(self._get_transform, self.get_params(opt_state))()
 
-    def sample_posterior(self, rng, opt_state, *args, **kwargs):
-        sample_shape = kwargs.pop('sample_shape', ())
-        base_dist = kwargs.pop('base_dist', None)
+    def sample_posterior(self, rng, opt_state, sample_shape=(), base_dist=None,
+                         model_args=None, model_kwargs=None):
         latent_size = np.size(self._init_latent)
         if base_dist is None:
             base_dist = _Normal(np.zeros(latent_size), 1.)
         params = self.get_params(opt_state)
-        latent_sample = substitute(seed(self._sample_latent, rng), params)(base_dist, sample_shape=sample_shape)
-        return self.unpack_latent(latent_sample)
+        latent_sample = substitute(seed(self._sample_latent, rng), params)(
+            base_dist, sample_shape=sample_shape)
+        return self._unpack_and_transform(latent_sample, params,
+                                          model_args=model_args, model_kwargs=model_kwargs)
 
 
 class AutoDiagonalNormal(AutoContinuous):
@@ -260,7 +277,7 @@ def _get_transform(self):
 
     def _loc_scale(self):
         loc = param('{}_loc'.format(self.prefix), None)
-        scale = biject_to(constraints.positive)(param('{}_scale'.format(self.prefix), None))
+        scale = param('{}_scale'.format(self.prefix), None, constraint=constraints.positive)
         return loc, scale
 
     def setup(self, *args, **kwargs):
@@ -270,7 +287,7 @@ def setup(self, *args, **kwargs):
             '{}_scale'.format(self.prefix): np.ones(np.size(self._init_latent)),
         }
 
-    def median(self, opt_state):
+    def median(self, opt_state, model_args=None, model_kwargs=None):
         """
         Returns the posterior median value of each latent variable.
 
@@ -278,10 +295,11 @@ def median(self, opt_state):
         :return: A dict mapping sample site name to median tensor.
         :rtype: dict
         """
-        loc, _ = substitute(self._loc_scale, self.get_params(opt_state))()
-        return transform_fn(self._inv_transforms, self._unravel_fn(loc))
+        params = self.get_params(opt_state)
+        loc, _ = substitute(self._loc_scale, params)()
+        return self._unpack_and_transform(loc, params, model_args=model_args, model_kwargs=model_kwargs)
 
-    def quantiles(self, opt_state, quantiles):
+    def quantiles(self, opt_state, quantiles, model_args=None, model_kwargs=None):
         """
         Returns posterior quantiles each latent variable. Example::
 
@@ -293,14 +311,11 @@ def quantiles(self, opt_state, quantiles):
         :return: A dict mapping sample site name to a list of quantile values.
         :rtype: dict
         """
-        loc, scale = substitute(self._loc_scale, self.get_params(opt_state))()
-        result = {}
-        for q in quantiles:
-            latent = osp.norm(loc, scale).ppf(q)
-            for name, unconstrained_value in self._unravel_fn(latent).items():
-                transform = self._inv_transforms[name]
-                result.setdefault(name, []).append(transform(unconstrained_value))
-        return result
+        params = self.get_params(opt_state)
+        loc, scale = substitute(self._loc_scale, params)()
+        quantiles = np.array(quantiles)[..., None]
+        latent = dist.Normal(loc, scale).icdf(quantiles)
+        return self._unpack_and_transform(latent, params, model_args=model_args, model_kwargs=model_kwargs)
 
 
 # TODO: remove when to_event is supported
diff --git a/numpyro/distributions/continuous.py b/numpyro/distributions/continuous.py
index 90b9e16b9..3214fb618 100644
--- a/numpyro/distributions/continuous.py
+++ b/numpyro/distributions/continuous.py
@@ -643,6 +643,9 @@ def log_prob(self, value):
         value_scaled = (value - self.loc) / self.scale
         return -0.5 * value_scaled ** 2 - normalize_term
 
+    def icdf(self, q):
+        return self.loc + self.scale * ndtri(q)
+
     @property
     def mean(self):
         return np.broadcast_to(self.loc, self.batch_shape)
diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index ddc853f23..0196c741f 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -11,8 +11,8 @@
 import numpyro.distributions as dist
 from numpyro.distributions.constraints import biject_to, real, ComposeTransform
 from numpyro.distributions.util import cholesky_inverse
-from numpyro.handlers import seed, substitute, trace
-from numpyro.infer_util import log_density, transform_fn
+from numpyro.handlers import seed, trace
+from numpyro.infer_util import constrain_fn, log_density, transform_fn
 from numpyro.util import cond, fori_loop, while_loop
 
 AdaptWindow = namedtuple('AdaptWindow', ['start', 'end'])
@@ -726,16 +726,6 @@ def _potential_energy(params):
     return _potential_energy
 
 
-def make_constrain_fn(model, model_args, model_kwargs, inv_transforms):
-    def _constrain_fn(params):
-        params_constrained = transform_fn(inv_transforms, params)
-        substituted_model = substitute(model, base_param_map=params_constrained)
-        model_trace = trace(substituted_model).get_trace(*model_args, **model_kwargs)
-        return {k: model_trace[k]['value'] for k, v in params.items()}
-
-    return _constrain_fn
-
-
 def initialize_model(rng, model, *model_args, init_strategy='uniform', **model_kwargs):
     """
     Given a model with Pyro primitives, returns a function which, given
@@ -801,16 +791,16 @@ def single_chain_init(key, only_params=False):
 
         if has_transformed_dist:
             # we might want to replay the trace here
-            constrain_fn = make_constrain_fn(seeded_model, model_args, model_kwargs, inv_transforms)
+            constrain_fun = jax.partial(constrain_fn, seeded_model, model_args, model_kwargs, inv_transforms)
         else:
-            constrain_fn = jax.partial(transform_fn, inv_transforms)
+            constrain_fun = jax.partial(transform_fn, inv_transforms)
 
         if only_params:
             return init_params
         else:
             return (init_params,
                     potential_energy(seeded_model, model_args, model_kwargs, inv_transforms),
-                    constrain_fn)
+                    constrain_fun)
 
     if rng.ndim == 1:
         return single_chain_init(rng)
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index bd1bf8367..e8401d1aa 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -53,3 +53,10 @@ def transform_fn(transforms, params, invert=False):
         transforms = {k: v.inv for k, v in transforms.items()}
     return {k: transforms[k](v) if k in transforms else v
             for k, v in params.items()}
+
+
+def constrain_fn(model, model_args, model_kwargs, transforms, params):
+    params_constrained = transform_fn(transforms, params)
+    substituted_model = substitute(model, base_param_map=params_constrained)
+    model_trace = trace(substituted_model).get_trace(*model_args, **model_kwargs)
+    return {k: model_trace[k]['value'] for k, v in params.items() if k in model_trace}
diff --git a/numpyro/svi.py b/numpyro/svi.py
index 913c62389..b987bf2d9 100644
--- a/numpyro/svi.py
+++ b/numpyro/svi.py
@@ -18,8 +18,6 @@ def _seed(model, guide, rng):
 
 
 def svi(model, guide, loss, optim_init, optim_update, get_params, **kwargs):
-    constrain_fn = None
-
     """
     Stochastic Variational Inference given an ELBo loss objective.
 
@@ -129,6 +127,27 @@ def evaluate(rng, opt_state, model_args=(), guide_args=()):
     return init_fn, update_fn, evaluate
 
 
+# TODO: move this function to svi, rename it to get_params
+def get_param(opt_state, model, guide, get_params, constrain_fn, rng,
+              model_args=None, guide_args=None, **kwargs):
+    params = constrain_fn(get_params(opt_state))
+    model, guide = _seed(model, guide, rng)
+    if guide_args is not None:
+        guide = substitute(guide, base_param_map=params)
+        guide_trace = trace(guide).get_trace(*guide_args, **kwargs)
+        model_params = {k: v for k, v in params.items() if k not in guide_trace}
+        params = {k: guide_trace[k]['value'] if k in guide_trace else v
+                  for k, v in params.items()}
+
+        if model_args is not None:
+            model = substitute(replay(model, guide_trace), base_param_map=model_params)
+            model_trace = trace(model).get_trace(*model_args, **kwargs)
+            params = {k: model_trace[k]['value'] if k in model_params else v
+                      for k, v in params.items()}
+
+    return params
+
+
 def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn):
     """
     This is the most basic implementation of the Evidence Lower Bound, which is the
diff --git a/test/contrib/test_autoguide.py b/test/contrib/test_autoguide.py
index be9cc42db..ef1d23d6d 100644
--- a/test/contrib/test_autoguide.py
+++ b/test/contrib/test_autoguide.py
@@ -83,3 +83,31 @@ def body_fn(i, val):
     # test .sample_posterior method
     posterior_samples = guide.sample_posterior(random.PRNGKey(1), opt_state, sample_shape=(1000,))
     assert_allclose(np.mean(posterior_samples['coefs'], 0), true_coefs, rtol=0.1)
+
+
+def test_uniform_normal():
+    true_coef = 0.9
+    data = true_coef + random.normal(random.PRNGKey(0), (1000,))
+
+    def model(data):
+        alpha = sample('alpha', dist.Uniform(0, 1))
+        loc = sample('loc', dist.Uniform(0, alpha))
+        sample('obs', dist.Normal(loc, 0.1), obs=data)
+
+    opt_init, opt_update, get_params = optimizers.adam(0.01)
+    rng_guide, rng_init, rng_train = random.split(random.PRNGKey(1), 3)
+    guide = AutoDiagonalNormal(rng_guide, model, get_params)
+    svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params)
+    opt_state, constrain_fn = svi_init(rng_init, model_args=(data,), guide_args=(data,))
+
+    def body_fn(i, val):
+        opt_state_, rng_ = val
+        loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_, model_args=(data,), guide_args=(data,))
+        return opt_state_, rng_
+
+    opt_state, _ = fori_loop(0, 1000, body_fn, (opt_state, rng_train))
+    median = guide.median(opt_state)
+    assert_allclose(median['loc'], true_coef, rtol=0.05)
+    # test .quantile method
+    median = guide.quantiles(opt_state, [0.2, 0.5])
+    assert_allclose(median['loc'][1], true_coef, rtol=0.1)
diff --git a/test/test_svi.py b/test/test_svi.py
index efdabd625..c7b9d2106 100644
--- a/test/test_svi.py
+++ b/test/test_svi.py
@@ -7,7 +7,7 @@
 import numpyro.distributions as dist
 from numpyro.distributions import constraints
 from numpyro.handlers import param, sample
-from numpyro.svi import elbo, svi
+from numpyro.svi import elbo, get_param, svi
 from numpyro.util import fori_loop
 
 
@@ -39,3 +39,32 @@ def body_fn(i, val):
 
     params = constrain_fn(get_params(opt_state))
     assert_allclose(params['alpha_q'] / (params['alpha_q'] + params['beta_q']), 0.8, atol=0.05, rtol=0.05)
+
+
+def test_dynamic_constraints():
+    true_coef = 0.9
+    data = true_coef + random.normal(random.PRNGKey(0), (1000,))
+
+    def model(data):
+        # NB: model's constraints will play no effect
+        loc = param('loc', 0., constraint=constraints.interval(0, 0.5))
+        sample('obs', dist.Normal(loc, 0.1), obs=data)
+
+    def guide():
+        alpha = param('alpha', 0.5, constraint=constraints.unit_interval)
+        param('loc', 0, constraint=constraints.interval(0, alpha))
+
+    opt_init, opt_update, get_params = optimizers.adam(0.05)
+    svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params)
+    rng_init, rng_train = random.split(random.PRNGKey(1))
+    opt_state, constrain_fn = svi_init(rng_init, model_args=(data,))
+
+    def body_fn(i, val):
+        opt_state_, rng_ = val
+        loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_, model_args=(data,))
+        return opt_state_, rng_
+
+    opt_state, rng = fori_loop(0, 300, body_fn, (opt_state, rng_train))
+    params = get_param(opt_state, model, guide, get_params, constrain_fn, rng,
+                       guide_args=())
+    assert_allclose(params['loc'], true_coef, atol=0.05)

From 25b240838cc27637aeb570e6d27bebdd1b4cf936 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sun, 4 Aug 2019 23:19:55 -0400
Subject: [PATCH 12/35] swap actual and expected in test

---
 test/test_hmc_util.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index 864529749..9c3893c73 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -421,7 +421,7 @@ def model():
 
     assert_allclose(expected_samples['x'], actual_samples['x'])
     assert_allclose(expected_samples['y'], actual_samples['y'])
-    assert_allclose(expected_potential_energy, actual_potential_energy)
+    assert_allclose(actual_potential_energy, expected_potential_energy)
 
 
 @pytest.mark.parametrize('init_strategy', ['prior', 'uniform'])

From 76a89f408d63f4fdeb84ad2e128548fec891848f Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 5 Aug 2019 12:27:22 -0400
Subject: [PATCH 13/35] address comment

---
 numpyro/svi.py | 19 +++++++++----------
 1 file changed, 9 insertions(+), 10 deletions(-)

diff --git a/numpyro/svi.py b/numpyro/svi.py
index b987bf2d9..8a57316c4 100644
--- a/numpyro/svi.py
+++ b/numpyro/svi.py
@@ -6,7 +6,7 @@
 from numpyro.contrib.autoguide import AutoContinuous
 from numpyro.distributions import constraints
 from numpyro.distributions.constraints import biject_to, ComposeTransform
-from numpyro.handlers import replay, seed, substitute, trace, Messenger
+from numpyro.handlers import replay, seed, substitute, trace
 from numpyro.infer_util import log_density, transform_fn
 
 
@@ -35,6 +35,9 @@ def svi(model, guide, loss, optim_init, optim_update, get_params, **kwargs):
     :return: tuple of `(init_fn, update_fn, evaluate)`.
     """
     constrain_fn = None
+    # NB: only skip transforms for AutoContinuous guide
+    loss_fn = jax.partial(loss, skip_dist_transforms=True) if isinstance(guide, AutoContinuous) \
+        else loss
 
     def init_fn(rng, model_args=(), guide_args=(), params=None):
         """
@@ -95,8 +98,8 @@ def update_fn(i, rng, opt_state, model_args=(), guide_args=()):
         rng, rng_seed = random.split(rng)
         model_init, guide_init = _seed(model, guide, rng_seed)
         params = get_params(opt_state)
-        loss_val, grads = value_and_grad(loss)(params, model_init, guide_init, model_args,
-                                               guide_args, kwargs, constrain_fn=constrain_fn)
+        loss_val, grads = value_and_grad(loss_fn)(params, model_init, guide_init, model_args,
+                                                  guide_args, kwargs, constrain_fn=constrain_fn)
         opt_state = optim_update(i, grads, opt_state)
         return loss_val, opt_state, rng
 
@@ -115,7 +118,7 @@ def evaluate(rng, opt_state, model_args=(), guide_args=()):
         """
         model_init, guide_init = _seed(model, guide, rng)
         params = get_params(opt_state)
-        return loss(params, model_init, guide_init, model_args, guide_args, kwargs, constrain_fn=constrain_fn)
+        return loss_fn(params, model_init, guide_init, model_args, guide_args, kwargs, constrain_fn=constrain_fn)
 
     # Make local functions visible from the global scope once
     # `svi` is called for sphinx doc generation.
@@ -148,7 +151,8 @@ def get_param(opt_state, model, guide, get_params, constrain_fn, rng,
     return params
 
 
-def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn):
+def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn,
+         skip_dist_transforms=False):
     """
     This is the most basic implementation of the Evidence Lower Bound, which is the
     fundamental objective in Variational Inference. This implementation has various
@@ -176,11 +180,6 @@ def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn):
     guide_log_density, guide_trace = log_density(guide, guide_args, kwargs, param_map)
     # NB: we only want to substitute params not available in guide_trace
     param_map = {k: v for k, v in param_map.items() if k not in guide_trace}
-    # NB: only skip transforms for AutoContinuous guide
-    skip_dist_transforms = False
-    guide_fn = guide.fn if isinstance(guide, Messenger) else guide
-    if isinstance(guide_fn, AutoContinuous):
-        skip_dist_transforms = True
     model_log_density, _ = log_density(replay(model, guide_trace), model_args, kwargs, param_map,
                                        skip_dist_transforms=skip_dist_transforms)
     # log p(z) - log q(z)

From c392565f0301fdff9df0bb64014dd95f26d4e4e4 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 5 Aug 2019 14:20:37 -0400
Subject: [PATCH 14/35] fix issue at elbo loss, at test for autoguide

---
 numpyro/handlers.py            |  2 --
 numpyro/svi.py                 | 20 +++++++++++------
 test/contrib/test_autoguide.py | 41 ++++++++++++++++++++++++++++++++++
 3 files changed, 54 insertions(+), 9 deletions(-)

diff --git a/numpyro/handlers.py b/numpyro/handlers.py
index 4ce4931e1..5c12969a3 100644
--- a/numpyro/handlers.py
+++ b/numpyro/handlers.py
@@ -196,8 +196,6 @@ def __init__(self, fn, guide_trace):
     def process_message(self, msg):
         if msg['name'] in self.guide_trace:
             msg['value'] = self.guide_trace[msg['name']]['value']
-            if msg['type'] == 'sample':
-                msg['intermediates'] = self.guide_trace[msg['name']]['intermediates']
 
 
 class block(Messenger):
diff --git a/numpyro/svi.py b/numpyro/svi.py
index 8a57316c4..dea002310 100644
--- a/numpyro/svi.py
+++ b/numpyro/svi.py
@@ -36,8 +36,7 @@ def svi(model, guide, loss, optim_init, optim_update, get_params, **kwargs):
     """
     constrain_fn = None
     # NB: only skip transforms for AutoContinuous guide
-    loss_fn = jax.partial(loss, skip_dist_transforms=True) if isinstance(guide, AutoContinuous) \
-        else loss
+    loss_fn = jax.partial(loss, is_autoguide=True) if isinstance(guide, AutoContinuous) else loss
 
     def init_fn(rng, model_args=(), guide_args=(), params=None):
         """
@@ -152,7 +151,7 @@ def get_param(opt_state, model, guide, get_params, constrain_fn, rng,
 
 
 def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn,
-         skip_dist_transforms=False):
+         is_autoguide=False):
     """
     This is the most basic implementation of the Evidence Lower Bound, which is the
     fundamental objective in Variational Inference. This implementation has various
@@ -178,10 +177,17 @@ def elbo(param_map, model, guide, model_args, guide_args, kwargs, constrain_fn,
     """
     param_map = constrain_fn(param_map)
     guide_log_density, guide_trace = log_density(guide, guide_args, kwargs, param_map)
-    # NB: we only want to substitute params not available in guide_trace
-    param_map = {k: v for k, v in param_map.items() if k not in guide_trace}
-    model_log_density, _ = log_density(replay(model, guide_trace), model_args, kwargs, param_map,
-                                       skip_dist_transforms=skip_dist_transforms)
+    if is_autoguide:
+        # in autoguide, a site's value holds intermediate value
+        for name, site in guide_trace.items():
+            if site['type'] == 'sample':
+                param_map[name] = site['value']
+    else:
+        # NB: we only want to substitute params not available in guide_trace
+        param_map = {k: v for k, v in param_map.items() if k not in guide_trace}
+        model = replay(model, guide_trace)
+    model_log_density, _ = log_density(model, model_args, kwargs, param_map,
+                                       skip_dist_transforms=is_autoguide)
     # log p(z) - log q(z)
     elbo = model_log_density - guide_log_density
     # Return (-elbo) since by convention we do gradient descent on a loss and
diff --git a/test/contrib/test_autoguide.py b/test/contrib/test_autoguide.py
index ef1d23d6d..3f7b74e89 100644
--- a/test/contrib/test_autoguide.py
+++ b/test/contrib/test_autoguide.py
@@ -4,6 +4,7 @@
 from jax import random
 from jax.experimental import optimizers
 import jax.numpy as np
+from jax.test_util import check_eq
 
 from numpyro.contrib.autoguide import AutoDiagonalNormal, AutoIAFNormal
 import numpyro.distributions as dist
@@ -111,3 +112,43 @@ def body_fn(i, val):
     # test .quantile method
     median = guide.quantiles(opt_state, [0.2, 0.5])
     assert_allclose(median['loc'][1], true_coef, rtol=0.1)
+
+
+def test_dynamic_supports():
+    true_coef = 0.9
+    data = true_coef + random.normal(random.PRNGKey(0), (1000,))
+
+    def actual_model(data):
+        alpha = sample('alpha', dist.Uniform(0, 1))
+        loc = sample('loc', dist.Uniform(0, alpha))
+        sample('obs', dist.Normal(loc, 0.1), obs=data)
+
+    def expected_model(data):
+        alpha = sample('alpha', dist.Uniform(0, 1))
+        loc = sample('loc', dist.Uniform(0, 1)) * alpha
+        sample('obs', dist.Normal(loc, 0.1), obs=data)
+
+    opt_init, opt_update, get_params = optimizers.adam(0.01)
+    rng_guide, rng_init, rng_train = random.split(random.PRNGKey(1), 3)
+
+    guide = AutoDiagonalNormal(rng_guide, actual_model, get_params)
+    svi_init, _, svi_eval = svi(actual_model, guide, elbo, opt_init, opt_update, get_params)
+    opt_state, constrain_fn = svi_init(rng_init, (data,), (data,))
+    actual_params = get_params(opt_state)
+    actual_base_values = constrain_fn(actual_params)
+    actual_values = guide.median(opt_state)
+    actual_loss = svi_eval(random.PRNGKey(1), opt_state, (data,), (data,))
+
+    guide = AutoDiagonalNormal(rng_guide, expected_model, get_params)
+    svi_init, _, svi_eval = svi(expected_model, guide, elbo, opt_init, opt_update, get_params)
+    opt_state, constrain_fn = svi_init(rng_init, (data,), (data,))
+    expected_params = get_params(opt_state)
+    expected_base_values = constrain_fn(expected_params)
+    expected_values = guide.median(opt_state)
+    expected_loss = svi_eval(random.PRNGKey(1), opt_state, (data,), (data,))
+
+    check_eq(actual_params, expected_params)
+    check_eq(actual_base_values, expected_base_values)
+    assert_allclose(actual_values['alpha'], expected_values['alpha'])
+    assert_allclose(actual_values['loc'], expected_values['alpha'] * expected_values['loc'])
+    assert_allclose(actual_loss, expected_loss)

From 75bb0a9c835cdfc499f1642405bac6f2f811cbc6 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Mon, 5 Aug 2019 14:38:25 -0400
Subject: [PATCH 15/35] fix import at hmc_util test

---
 test/test_hmc_util.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index 9c3893c73..73ee89a68 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -23,14 +23,13 @@
     dual_averaging,
     find_reasonable_step_size,
     initialize_model,
-    make_constrain_fn,
     parametric_draws,
     potential_energy,
     velocity_verlet,
     warmup_adapter,
     welford_covariance
 )
-from numpyro.infer_util import transform_fn
+from numpyro.infer_util import constrain_fn, transform_fn
 from numpyro.util import control_flow_prims_disabled, fori_loop, optional
 
 logger = logging.getLogger(__name__)
@@ -415,8 +414,8 @@ def model():
     )
 
     base_inv_transforms = {'x': biject_to(x_prior.support), 'y': biject_to(y_prior.base_dist.support)}
-    actual_samples = make_constrain_fn(
-        seed(model, random.PRNGKey(0)), (), {}, base_inv_transforms)(params)
+    actual_samples = constrain_fn(
+        seed(model, random.PRNGKey(0)), (), {}, base_inv_transforms, params)
     actual_potential_energy = potential_energy(model, (), {}, base_inv_transforms)(params)
 
     assert_allclose(expected_samples['x'], actual_samples['x'])

From f33c0cf589d2c30343d462f148daa0a6394fe485 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Tue, 6 Aug 2019 22:17:59 -0400
Subject: [PATCH 16/35] use cov instead of np.cov, defer the change to later PR

---
 numpyro/hmc_util.py   | 14 +++++++++++---
 test/test_hmc_util.py |  3 ++-
 2 files changed, 13 insertions(+), 4 deletions(-)

diff --git a/numpyro/hmc_util.py b/numpyro/hmc_util.py
index 16bb42ddf..9e90346b0 100644
--- a/numpyro/hmc_util.py
+++ b/numpyro/hmc_util.py
@@ -13,7 +13,7 @@
 from numpyro.distributions.util import cholesky_inverse
 from numpyro.handlers import seed, trace
 from numpyro.infer_util import constrain_fn, find_valid_initial_params, init_to_uniform, potential_energy, transform_fn
-from numpyro.util import cond, while_loop
+from numpyro.util import cond, fori_loop, while_loop
 
 AdaptWindow = namedtuple('AdaptWindow', ['start', 'end'])
 AdaptState = namedtuple('AdaptState', ['step_size', 'inverse_mass_matrix', 'mass_matrix_sqrt',
@@ -776,6 +776,14 @@ def single_chain_init(key):
     return init_params, potential_fn, constrain_fun
 
 
+# TODO: to be replaced by np.cov ddof=1 for the next JAX version
+def _cov(samples):
+    wc_init, wc_update, wc_final = welford_covariance(diagonal=False)
+    state = wc_init(samples.shape[1])
+    state = fori_loop(0, samples.shape[0], lambda i, state: wc_update(samples[i], state), state)
+    return wc_final(state)[0]
+
+
 def consensus(subposteriors, num_draws=None, diagonal=False, rng=None):
     """
     Merges subposteriors following consensus Monte Carlo algorithm.
@@ -815,7 +823,7 @@ def consensus(subposteriors, num_draws=None, diagonal=False, rng=None):
         # get weighted samples
         samples_flat = np.einsum('ij,ikj->kj', normalized_weights, joined_subposteriors)
     else:
-        weights = vmap(lambda x: np.linalg.inv(np.cov(x)))(joined_subposteriors)
+        weights = vmap(lambda x: np.linalg.inv(_cov(x)))(joined_subposteriors)
         normalized_weights = np.matmul(np.linalg.inv(np.sum(weights, axis=0)), weights)
         samples_flat = np.einsum('ijk,ilk->lj', normalized_weights, joined_subposteriors)
 
@@ -853,7 +861,7 @@ def parametric(subposteriors, diagonal=False):
         mean = np.einsum('ij,ij->j', normalized_weights, submeans)
         return mean, var
     else:
-        weights = vmap(lambda x: np.linalg.inv(np.cov(x)))(joined_subposteriors)
+        weights = vmap(lambda x: np.linalg.inv(_cov(x)))(joined_subposteriors)
         cov = np.linalg.inv(np.sum(weights, axis=0))
         normalized_weights = np.matmul(cov, weights)
 
diff --git a/test/test_hmc_util.py b/test/test_hmc_util.py
index 3189e468c..c0a23d499 100644
--- a/test/test_hmc_util.py
+++ b/test/test_hmc_util.py
@@ -14,6 +14,7 @@
 from numpyro.handlers import sample, seed
 from numpyro.hmc_util import (
     AdaptWindow,
+    _cov,
     _is_iterative_turning,
     _leaf_idx_to_ckpt_idxs,
     build_adaptation_schedule,
@@ -511,7 +512,7 @@ def test_gaussian_subposterior(method, diagonal):
     if diagonal:
         assert_allclose(np.var(draws, axis=0), np.diag(cov), atol=0.05)
     else:
-        assert_allclose(np.cov(draws), cov, atol=0.05)
+        assert_allclose(_cov(draws), cov, atol=0.05)
 
 
 @pytest.mark.parametrize('method', [consensus, parametric_draws])

From 240399b37ff9730be7f9e1f3d00e047277e7efc3 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Tue, 6 Aug 2019 23:02:53 -0400
Subject: [PATCH 17/35] add option param_as_improper

---
 numpyro/handlers.py   | 15 ++++++++++++---
 numpyro/infer_util.py | 24 +++++++++++++++---------
 test/test_handlers.py |  2 +-
 3 files changed, 28 insertions(+), 13 deletions(-)

diff --git a/numpyro/handlers.py b/numpyro/handlers.py
index 5c12969a3..1559cfb49 100644
--- a/numpyro/handlers.py
+++ b/numpyro/handlers.py
@@ -391,9 +391,18 @@ def process_message(self, msg):
                     else:
                         msg['value'] = self.base_param_map[msg['name']]
         elif self.substitute_fn is not None:
-            value = self.substitute_fn(msg)
-            if value is not None:
-                msg['value'] = value
+            base_value = self.substitute_fn(msg)
+            if base_value is not None:
+                if msg['type'] == 'sample':
+                    msg['value'], msg['intermediates'] = msg['fn'].transform_with_intermediates(
+                        base_value)
+                else:
+                    constraint = msg['kwargs'].pop('constraint', real)
+                    transform = biject_to(constraint)
+                    if isinstance(transform, ComposeTransform):
+                        msg['value'] = ComposeTransform(transform.parts[1:])(base_value)
+                    else:
+                        msg['value'] = base_value
         else:
             raise ValueError("Neither `param_map`, `base_param_map`, nor `substitute_fn`"
                              "provided to substitute handler.")
diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index d553125bf..92a819527 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -109,11 +109,12 @@ def potential_energy(model, model_args, model_kwargs, inv_transforms, params):
     return - log_joint
 
 
-def init_to_median(site, num_samples=15):
+def init_to_median(site, num_samples=15, skip_param=False):
     """
     Initialize to the prior median.
     """
-    if site['is_observed']:
+    if ((site['type'] == 'sample' and site['is_observed'])
+            or (site['type'] == 'param' and skip_param)):
         return None
     samples = sample('_init', site['fn'], sample_shape=(num_samples,))
     # TODO: use np.median when it is available upstream
@@ -121,21 +122,23 @@ def init_to_median(site, num_samples=15):
     return value
 
 
-def init_to_prior(site):
+def init_to_prior(site, skip_param=False):
     """
     Initialize to a prior sample.
     """
-    if site['is_observed']:
+    if ((site['type'] == 'sample' and site['is_observed'])
+            or (site['type'] == 'param' and skip_param)):
         return None
     return sample('_init', site['fn'])
 
 
-def init_to_uniform(site, radius=2):
+def init_to_uniform(site, radius=2, skip_param=False):
     """
     Initialize to an arbitrary feasible point, ignoring distribution
     parameters.
     """
-    if site['is_observed']:
+    if ((site['type'] == 'sample' and site['is_observed'])
+            or (site['type'] == 'param' and skip_param)):
         return None
     value = sample('_init', site['fn'])
     t = biject_to(site['fn'].support)
@@ -144,12 +147,13 @@ def init_to_uniform(site, radius=2):
     return t(unconstrained_value)
 
 
-def init_to_feasible(site):
+def init_to_feasible(site, skip_param=False):
     """
     Initialize to an arbitrary feasible point, ignoring distribution
     parameters.
     """
-    if site['is_observed']:
+    if ((site['type'] == 'sample' and site['is_observed'])
+            or (site['type'] == 'param' and skip_param)):
         return None
     value = sample('_init', site['fn'])
     t = biject_to(site['fn'].support)
@@ -174,6 +178,8 @@ def find_valid_initial_params(rng, model, *model_args, init_strategy=init_to_uni
     :param `**model_kwargs`: kwargs provided to the model.
     :return: tuple of (`init_params`, `is_valid`).
     """
+    init_strategy = jax.partial(init_strategy, skip_param=not param_as_improper)
+
     def cond_fn(state):
         i, _, _, is_valid = state
         return (i < 100) & (~is_valid)
@@ -195,7 +201,7 @@ def body_fn(state):
                 else:
                     constrained_values[k] = v['value']
                     inv_transforms[k] = biject_to(v['fn'].support)
-            elif v['type'] == 'param':
+            elif v['type'] == 'param' and param_as_improper:
                 constraint = v['kwargs'].pop('constraint', real)
                 transform = biject_to(constraint)
                 if isinstance(transform, ComposeTransform):
diff --git a/test/test_handlers.py b/test/test_handlers.py
index 2437eb5af..8a7c0ac81 100644
--- a/test/test_handlers.py
+++ b/test/test_handlers.py
@@ -5,7 +5,7 @@
 
 import numpyro.distributions as dist
 from numpyro.handlers import sample, scale, param, substitute, seed, trace, condition
-from numpyro.hmc_util import log_density
+from numpyro.infer_util import log_density
 from numpyro.util import optional
 
 

From 92293cc315843a78b717951bdb19af938c1b28bf Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 7 Aug 2019 00:23:52 -0400
Subject: [PATCH 18/35] support param as improper

---
 numpyro/infer_util.py | 68 +++++++++++++++++++++++++++----------------
 1 file changed, 43 insertions(+), 25 deletions(-)

diff --git a/numpyro/infer_util.py b/numpyro/infer_util.py
index 92a819527..1e2b38208 100644
--- a/numpyro/infer_util.py
+++ b/numpyro/infer_util.py
@@ -113,23 +113,31 @@ def init_to_median(site, num_samples=15, skip_param=False):
     """
     Initialize to the prior median.
     """
-    if ((site['type'] == 'sample' and site['is_observed'])
-            or (site['type'] == 'param' and skip_param)):
-        return None
-    samples = sample('_init', site['fn'], sample_shape=(num_samples,))
-    # TODO: use np.median when it is available upstream
-    value = np.mean(samples, axis=0)
-    return value
+    if site['type'] == 'sample' and not site['is_observed']:
+        if isinstance(site['fn'], dist.TransformedDistribution):
+            fn = site['fn'].base_dist
+        else:
+            fn = site['fn']
+        samples = sample('_init', fn, sample_shape=(num_samples,))
+        # TODO: use np.median when it is available upstream
+        return np.mean(samples, axis=0)
+
+    if site['type'] == 'param' and not skip_param:
+        # return base value of param site
+        constraint = site['kwargs'].pop('constraint', real)
+        transform = biject_to(constraint)
+        value = site['args'][0]
+        if isinstance(transform, ComposeTransform):
+            base_transform = transform.parts[0]
+            value = base_transform(transform.inv(value))
+        return value
 
 
 def init_to_prior(site, skip_param=False):
     """
     Initialize to a prior sample.
     """
-    if ((site['type'] == 'sample' and site['is_observed'])
-            or (site['type'] == 'param' and skip_param)):
-        return None
-    return sample('_init', site['fn'])
+    return init_to_median(site, num_samples=1, skip_param=skip_param)
 
 
 def init_to_uniform(site, radius=2, skip_param=False):
@@ -137,14 +145,29 @@ def init_to_uniform(site, radius=2, skip_param=False):
     Initialize to an arbitrary feasible point, ignoring distribution
     parameters.
     """
-    if ((site['type'] == 'sample' and site['is_observed'])
-            or (site['type'] == 'param' and skip_param)):
-        return None
-    value = sample('_init', site['fn'])
-    t = biject_to(site['fn'].support)
-    unconstrained_value = sample('_unconstrained_init', dist.Uniform(-radius, radius),
-                                 sample_shape=np.shape(t.inv(value)))
-    return t(unconstrained_value)
+    if site['type'] == 'sample' and not site['is_observed']:
+        if isinstance(site['fn'], dist.TransformedDistribution):
+            fn = site['fn'].base_dist
+        else:
+            fn = site['fn']
+        value = sample('_init', fn)
+        base_transform = biject_to(fn.support)
+        unconstrained_value = sample('_unconstrained_init', dist.Uniform(-radius, radius),
+                                     sample_shape=np.shape(base_transform.inv(value)))
+        return base_transform(unconstrained_value)
+
+    if site['type'] == 'param' and not skip_param:
+        # return base value of param site
+        constraint = site['kwargs'].pop('constraint', real)
+        transform = biject_to(constraint)
+        value = site['args'][0]
+        unconstrained_value = sample('_unconstrained_init', dist.Uniform(-radius, radius),
+                                     sample_shape=np.shape(transform.inv(value)))
+        if isinstance(transform, ComposeTransform):
+            base_transform = transform.parts[0]
+        else:
+            base_transform = transform
+        return base_transform(unconstrained_value)
 
 
 def init_to_feasible(site, skip_param=False):
@@ -152,12 +175,7 @@ def init_to_feasible(site, skip_param=False):
     Initialize to an arbitrary feasible point, ignoring distribution
     parameters.
     """
-    if ((site['type'] == 'sample' and site['is_observed'])
-            or (site['type'] == 'param' and skip_param)):
-        return None
-    value = sample('_init', site['fn'])
-    t = biject_to(site['fn'].support)
-    return t(np.zeros(np.shape(t.inv(value))))
+    return init_to_uniform(site, radius=0, skip_param=skip_param)
 
 
 def find_valid_initial_params(rng, model, *model_args, init_strategy=init_to_uniform,

From 3d5d1e8d70c3e1b392d2547ebe3731bf290c9346 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Thu, 8 Aug 2019 00:26:00 -0400
Subject: [PATCH 19/35] add covtype notebook

---
 notebooks/source/covtype.ipynb | 2705 ++++++++++++++++++++++++++++++++
 1 file changed, 2705 insertions(+)
 create mode 100644 notebooks/source/covtype.ipynb

diff --git a/notebooks/source/covtype.ipynb b/notebooks/source/covtype.ipynb
new file mode 100644
index 000000000..e3975a88b
--- /dev/null
+++ b/notebooks/source/covtype.ipynb
@@ -0,0 +1,2705 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from functools import partial\n",
+    "import os; os.environ['XLA_FLAGS'] = '--xla_force_host_platform_device_count=4'\n",
+    "\n",
+    "import numpy as onp\n",
+    "\n",
+    "from jax import jit, random, vmap\n",
+    "from jax.config import config; config.update('jax_platform_name', 'cpu')\n",
+    "import jax.numpy as np\n",
+    "\n",
+    "import numpyro.distributions as dist\n",
+    "from numpyro.examples.datasets import COVTYPE, load_dataset\n",
+    "from numpyro.handlers import sample, scale, seed, substitute, trace\n",
+    "from numpyro.hmc_util import consensus, initialize_model, parametric_draws\n",
+    "from numpyro.mcmc import mcmc"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### load data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Data shape: (581012, 55)\n",
+      "Label distribution: 211840 has label 1, 369172 has label 0\n"
+     ]
+    }
+   ],
+   "source": [
+    "def _load_dataset():\n",
+    "    _, fetch = load_dataset(COVTYPE, shuffle=False)\n",
+    "    features, labels = fetch()\n",
+    "\n",
+    "    # normalize features and add intercept\n",
+    "    features = (features - features.mean(0)) / features.std(0)\n",
+    "    features = np.hstack([features, np.ones((features.shape[0], 1))])\n",
+    "\n",
+    "    # make binary feature\n",
+    "    _, counts = onp.unique(labels, return_counts=True)\n",
+    "    specific_category = np.argmax(counts)\n",
+    "    labels = (labels == specific_category)\n",
+    "\n",
+    "    N, dim = features.shape\n",
+    "    print(\"Data shape:\", features.shape)\n",
+    "    print(\"Label distribution: {} has label 1, {} has label 0\"\n",
+    "          .format(labels.sum(), N - labels.sum()))\n",
+    "    return features, labels\n",
+    "\n",
+    "X_full, y_full = _load_dataset()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### prepare train shards and test set"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Train set contains 400000 (68.85%) data points.\n",
+      "Test set contains 181012 (31.15%) data points.\n"
+     ]
+    }
+   ],
+   "source": [
+    "def get_train_shards_and_test_data(X, y, K, N, rng=None):\n",
+    "    if rng is not None:\n",
+    "        idxs = random.shuffle(rng, np.arange(X.shape[0]))\n",
+    "        X = X[idxs]\n",
+    "        y = y[idxs]\n",
+    "    shards = []\n",
+    "    for i in range(K):\n",
+    "        shards.append((X[i * N: (i + 1) * N], y[i * N: (i + 1) * N]))\n",
+    "    test_data = (X[K * N:], y[K * N:])\n",
+    "    return shards, test_data\n",
+    "\n",
+    "K, N = 40, 10000\n",
+    "shards, (X_test, y_test) = get_train_shards_and_test_data(\n",
+    "    X_full, y_full, K, N, random.PRNGKey(0))\n",
+    "print(\"Train set contains {} ({}%) data points.\".format(\n",
+    "    K * N, round(K * N / X_full.shape[0] * 100, 2)))\n",
+    "print(\"Test set contains {} ({}%) data points.\".format(\n",
+    "    X_full.shape[0] - K * N, round(100 - K * N / X_full.shape[0] * 100, 2)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def model(X, y, K=1):\n",
+    "    with scale(1 / K):\n",
+    "        coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
+    "    return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### sampling"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_subposterior(rng, shard, K):\n",
+    "    rngs = random.split(rng, 4)\n",
+    "    X, y = shard\n",
+    "    init_params, potential_fn, _ = initialize_model(rngs, model, X, y, K=K)\n",
+    "    samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
+    "                   num_chains=4, potential_fn=potential_fn)\n",
+    "    return samples"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      " =============================== SUBPOSTERIOR 00 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.94      0.06      1.94      1.84      2.04  10596.19      1.00\n",
+      "  coefs[1]      0.00      0.03      0.00     -0.06      0.06  13018.15      1.00\n",
+      "  coefs[2]     -0.05      0.07     -0.05     -0.15      0.06   3962.76      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   8349.60      1.00\n",
+      "  coefs[4]     -0.13      0.04     -0.13     -0.19     -0.07   9673.05      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.15     -0.04  11774.95      1.00\n",
+      "  coefs[6]      0.33      0.25      0.32     -0.08      0.73   3044.25      1.00\n",
+      "  coefs[7]     -0.70      0.15     -0.69     -0.94     -0.45   3230.34      1.00\n",
+      "  coefs[8]      0.61      0.29      0.60      0.12      1.08   3048.04      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.01  11912.89      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.66      1.50   3045.41      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.42   3041.88      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.99      1.17   3040.15      1.00\n",
+      " coefs[13]     -0.94      0.65     -0.88     -2.00      0.08   5089.97      1.00\n",
+      " coefs[14]     -0.48      0.67     -0.37     -1.51      0.56   5935.95      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.69     -1.65      0.03   5174.92      1.00\n",
+      " coefs[16]     -0.71      0.60     -0.59     -1.63      0.11   4779.67      1.00\n",
+      " coefs[17]     -0.28      0.22     -0.27     -0.65      0.08   1027.92      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.46     -1.58      0.40   5873.46      1.00\n",
+      " coefs[19]     -0.49      0.67     -0.39     -1.61      0.53   5699.48      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.03   5339.04      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1357.53      1.00\n",
+      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11   1117.18      1.00\n",
+      " coefs[23]     -0.07      0.25     -0.07     -0.47      0.34    537.29      1.00\n",
+      " coefs[24]     -0.04      0.16     -0.04     -0.31      0.21    542.14      1.00\n",
+      " coefs[25]     -0.01      0.23     -0.02     -0.39      0.35    498.36      1.00\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.31      0.27    506.74      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.12   5016.54      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.71  11735.13      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.04      0.21    522.46      1.00\n",
+      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    581.10      1.00\n",
+      " coefs[31]      0.04      0.08      0.04     -0.09      0.16    822.05      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.03      0.26    518.96      1.00\n",
+      " coefs[33]      0.13      0.13      0.13     -0.08      0.34    494.96      1.00\n",
+      " coefs[34]      0.06      0.05      0.06     -0.02      0.15    858.21      1.00\n",
+      " coefs[35]      0.38      0.24      0.38     -0.01      0.77    488.03      1.00\n",
+      " coefs[36]      0.40      0.31      0.40     -0.10      0.90    484.06      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.13      0.50    491.13      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05    833.97      1.00\n",
+      " coefs[39]     -0.01      0.08     -0.01     -0.14      0.11    601.79      1.00\n",
+      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    632.43      1.00\n",
+      " coefs[41]     -0.77      0.58     -0.65     -1.62      0.05   5172.22      1.00\n",
+      " coefs[42]      0.11      0.41      0.11     -0.56      0.77    485.90      1.00\n",
+      " coefs[43]     -0.04      0.23     -0.04     -0.40      0.34    487.10      1.00\n",
+      " coefs[44]      0.16      0.21      0.16     -0.19      0.50    486.21      1.00\n",
+      " coefs[45]      0.12      0.30      0.12     -0.36      0.61    485.58      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.26      0.64    488.71      1.00\n",
+      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    688.12      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    530.56      1.00\n",
+      " coefs[49]      0.02      1.00      0.01     -1.59      1.68  11841.74      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4715.49      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.17    496.97      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    491.79      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    498.09      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4068.47      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 01 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.03      0.06      2.03      1.93      2.13   6297.01      1.00\n",
+      "  coefs[1]     -0.10      0.03     -0.10     -0.16     -0.05   6696.79      1.00\n",
+      "  coefs[2]     -0.04      0.07     -0.04     -0.16      0.09   2407.61      1.00\n",
+      "  coefs[3]     -0.23      0.03     -0.24     -0.29     -0.18   5620.77      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   5804.19      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13   6953.33      1.00\n",
+      "  coefs[6]      0.23      0.30      0.23     -0.26      0.72   2060.03      1.00\n",
+      "  coefs[7]     -0.64      0.18     -0.64     -0.94     -0.34   2165.40      1.00\n",
+      "  coefs[8]      0.68      0.35      0.67      0.11      1.27   2051.67      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.02   7364.88      1.00\n",
+      " coefs[10]      0.42      0.65      0.42     -0.69      1.45   2455.62      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.05     -0.54      0.41   2496.49      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -1.06      1.08   2474.35      1.00\n",
+      " coefs[13]     -1.02      0.64     -0.97     -2.04      0.02   3633.72      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.36     -1.51      0.55   3974.22      1.00\n",
+      " coefs[15]     -0.78      0.56     -0.68     -1.61      0.05   3326.03      1.00\n",
+      " coefs[16]     -0.74      0.58     -0.63     -1.61      0.10   3931.39      1.00\n",
+      " coefs[17]     -0.11      0.18     -0.10     -0.41      0.20    716.27      1.01\n",
+      " coefs[18]     -0.54      0.67     -0.44     -1.55      0.44   4309.01      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.35     -1.56      0.59   4171.46      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   3801.33      1.00\n",
+      " coefs[21]      0.03      0.03      0.03     -0.01      0.07    928.09      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    821.22      1.01\n",
+      " coefs[23]      0.03      0.24      0.04     -0.38      0.40    486.42      1.01\n",
+      " coefs[24]      0.05      0.15      0.05     -0.20      0.29    508.69      1.01\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.43      0.31    474.61      1.01\n",
+      " coefs[26]      0.01      0.18      0.02     -0.27      0.31    482.02      1.01\n",
+      " coefs[27]     -0.68      0.63     -0.56     -1.60      0.18   3544.17      1.00\n",
+      " coefs[28]     -0.78      0.60     -0.66     -1.60      0.03   3720.32      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.03      0.21    525.53      1.01\n",
+      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    779.43      1.01\n",
+      " coefs[31]     -0.04      0.10     -0.03     -0.19      0.11   1169.81      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    512.40      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.37    482.55      1.01\n",
+      " coefs[34]      0.93      0.59      0.82      0.11      1.79   3574.15      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    473.55      1.01\n",
+      " coefs[36]      0.30      0.30      0.30     -0.21      0.78    470.35      1.01\n",
+      " coefs[37]      0.17      0.19      0.17     -0.16      0.47    467.05      1.01\n",
+      " coefs[38]     -0.04      0.04     -0.04     -0.11      0.02    769.86      1.01\n",
+      " coefs[39]      0.01      0.08      0.01     -0.11      0.14    578.20      1.01\n",
+      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.08    612.50      1.01\n",
+      " coefs[41]     -0.80      0.59     -0.67     -1.64      0.04   3531.23      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.64      0.68    469.07      1.01\n",
+      " coefs[43]      0.02      0.23      0.02     -0.35      0.39    472.51      1.01\n",
+      " coefs[44]      0.16      0.21      0.16     -0.19      0.49    471.76      1.01\n",
+      " coefs[45]      0.09      0.29      0.09     -0.40      0.55    469.03      1.01\n",
+      " coefs[46]      0.23      0.27      0.23     -0.22      0.67    471.88      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.04    839.36      1.01\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    510.68      1.01\n",
+      " coefs[49]      0.03      1.01      0.03     -1.59      1.76   7599.21      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.67     -0.07   3259.83      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.12    472.94      1.01\n",
+      " coefs[52]     -0.15      0.16     -0.15     -0.40      0.11    473.82      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.03    488.46      1.01\n",
+      " coefs[54]     -1.64      0.18     -1.63     -1.94     -1.34   2819.50      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 02 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.07  10141.39      1.00\n",
+      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.01  11681.33      1.00\n",
+      "  coefs[2]      0.05      0.08      0.05     -0.08      0.18   3349.04      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.22   8028.85      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.06   9352.06      1.00\n",
+      "  coefs[5]     -0.13      0.03     -0.13     -0.18     -0.07  11348.87      1.00\n",
+      "  coefs[6]      0.80      0.32      0.80      0.28      1.32   2779.37      1.00\n",
+      "  coefs[7]     -1.06      0.19     -1.06     -1.37     -0.74   2899.08      1.00\n",
+      "  coefs[8]      1.32      0.37      1.32      0.71      1.93   2786.07      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  12106.53      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.64      1.50   2853.02      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.39   2876.41      1.00\n",
+      " coefs[12]      0.13      0.65      0.13     -0.96      1.18   2851.32      1.00\n",
+      " coefs[13]     -1.08      0.62     -1.02     -2.08     -0.10   4547.27      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.56   5752.40      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.06   4399.13      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.58      0.16   5696.39      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.13     -0.44      0.18    742.08      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.58      0.39   5940.96      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.35     -1.54      0.62   5852.71      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5257.50      1.00\n",
+      " coefs[21]     -0.76      0.58     -0.64     -1.60      0.03   5145.51      1.00\n",
+      " coefs[22]      0.03      0.08      0.03     -0.08      0.16   1171.01      1.00\n",
+      " coefs[23]      0.16      0.25      0.15     -0.26      0.57    534.48      1.00\n",
+      " coefs[24]      0.02      0.16      0.02     -0.25      0.28    535.89      1.00\n",
+      " coefs[25]     -0.15      0.24     -0.16     -0.56      0.23    527.60      1.00\n",
+      " coefs[26]      0.06      0.18      0.06     -0.25      0.36    526.14      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.61      0.13   5205.52      1.00\n",
+      " coefs[28]      0.03      1.00      0.04     -1.61      1.65  10712.86      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    607.37      1.00\n",
+      " coefs[30]     -0.00      0.10     -0.00     -0.16      0.15    652.04      1.00\n",
+      " coefs[31]     -0.02      0.10     -0.01     -0.17      0.13   1134.64      1.00\n",
+      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    535.91      1.00\n",
+      " coefs[33]      0.15      0.14      0.15     -0.08      0.36    527.35      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4974.60      1.00\n",
+      " coefs[35]      0.38      0.25      0.38     -0.04      0.78    520.29      1.00\n",
+      " coefs[36]      0.37      0.32      0.37     -0.14      0.92    516.69      1.00\n",
+      " coefs[37]      0.18      0.20      0.17     -0.17      0.49    518.95      1.00\n",
+      " coefs[38]     -0.80      0.58     -0.68     -1.65     -0.01   5323.77      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    622.80      1.00\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    571.08      1.01\n",
+      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1236.93      1.00\n",
+      " coefs[42]      0.07      0.43      0.07     -0.61      0.79    513.79      1.00\n",
+      " coefs[43]      0.01      0.24      0.01     -0.38      0.41    521.37      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.21      0.52    511.80      1.00\n",
+      " coefs[45]      0.08      0.31      0.08     -0.43      0.58    514.38      1.00\n",
+      " coefs[46]      0.23      0.29      0.23     -0.23      0.71    515.12      1.00\n",
+      " coefs[47]     -0.13      0.09     -0.13     -0.27      0.01   1051.75      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    574.66      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.63      0.02   5085.05      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.07   4703.61      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.17    522.50      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.07     -0.34      0.20    518.37      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    526.44      1.00\n",
+      " coefs[54]     -1.67      0.19     -1.65     -1.95     -1.36   3894.03      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 03 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9308.68      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.04  11831.11      1.00\n",
+      "  coefs[2]     -0.08      0.06     -0.08     -0.18      0.03   3625.92      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.33     -0.22   7283.21      1.00\n",
+      "  coefs[4]     -0.09      0.03     -0.09     -0.14     -0.03   8157.44      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10004.68      1.00\n",
+      "  coefs[6]      0.04      0.24      0.04     -0.35      0.44   2665.26      1.00\n",
+      "  coefs[7]     -0.57      0.15     -0.57     -0.80     -0.31   2781.87      1.00\n",
+      "  coefs[8]      0.33      0.28      0.33     -0.12      0.80   2642.32      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11808.21      1.00\n",
+      " coefs[10]      0.37      0.65      0.37     -0.72      1.45   2985.63      1.00\n",
+      " coefs[11]     -0.00      0.29     -0.01     -0.48      0.49   2998.92      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2991.93      1.00\n",
+      " coefs[13]     -0.99      0.63     -0.92     -1.99      0.04   4876.03      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.53      0.50   5544.85      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.06   4454.60      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.60     -1.61      0.13   4989.00      1.00\n",
+      " coefs[17]      0.05      0.17      0.05     -0.23      0.32    633.85      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.54      0.43   5998.03      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.52      0.63   5489.12      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.61      0.02   5007.75      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1821.60      1.00\n",
+      " coefs[22]     -0.00      0.08      0.00     -0.13      0.11   1044.03      1.00\n",
+      " coefs[23]      0.02      0.26      0.02     -0.40      0.45    600.96      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.24      0.30    591.14      1.00\n",
+      " coefs[25]     -0.05      0.24     -0.05     -0.45      0.34    569.65      1.00\n",
+      " coefs[26]     -0.00      0.19     -0.00     -0.29      0.33    572.75      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   4787.94      1.00\n",
+      " coefs[28]      0.03      0.99      0.04     -1.57      1.67   9415.44      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    615.59      1.00\n",
+      " coefs[30]      0.03      0.10      0.03     -0.13      0.19    749.84      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.11      0.15    937.97      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    585.50      1.00\n",
+      " coefs[33]      0.14      0.14      0.14     -0.08      0.37    578.11      1.00\n",
+      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1184.94      1.00\n",
+      " coefs[35]      0.34      0.25      0.34     -0.08      0.75    562.89      1.00\n",
+      " coefs[36]      0.36      0.32      0.36     -0.15      0.92    562.32      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.51    564.23      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.10      0.03    914.20      1.00\n",
+      " coefs[39]     -0.83      0.57     -0.71     -1.68     -0.05   4856.42      1.00\n",
+      " coefs[40]      0.09      0.05      0.09     -0.00      0.17    716.14      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.66     -1.62      0.04   5147.75      1.00\n",
+      " coefs[42]      0.06      0.43      0.06     -0.63      0.80    560.74      1.00\n",
+      " coefs[43]      0.04      0.24      0.04     -0.36      0.44    567.24      1.00\n",
+      " coefs[44]      0.23      0.22      0.23     -0.14      0.59    562.82      1.00\n",
+      " coefs[45]      0.13      0.31      0.13     -0.38      0.65    562.89      1.00\n",
+      " coefs[46]      0.21      0.29      0.21     -0.26      0.69    560.89      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.07    884.93      1.00\n",
+      " coefs[48]     -0.01      0.07     -0.01     -0.11      0.11    642.70      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.66      0.01   4636.00      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.72     -1.68     -0.06   4578.95      1.00\n",
+      " coefs[51]     -0.07      0.18     -0.07     -0.36      0.22    573.25      1.00\n",
+      " coefs[52]     -0.11      0.17     -0.11     -0.39      0.15    567.32      1.00\n",
+      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.04    584.89      1.00\n",
+      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.43   3787.09      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 04 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9663.05      1.00\n",
+      "  coefs[1]      0.01      0.03      0.01     -0.04      0.07  12229.09      1.00\n",
+      "  coefs[2]     -0.05      0.08     -0.05     -0.18      0.08   3518.69      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.26     -0.32     -0.21   7811.88      1.00\n",
+      "  coefs[4]     -0.14      0.03     -0.14     -0.20     -0.09   8939.99      1.00\n",
+      "  coefs[5]     -0.21      0.03     -0.21     -0.26     -0.15  10756.10      1.00\n",
+      "  coefs[6]      0.29      0.32      0.28     -0.22      0.82   2819.50      1.00\n",
+      "  coefs[7]     -0.72      0.19     -0.72     -1.04     -0.41   2925.77      1.00\n",
+      "  coefs[8]      0.69      0.37      0.69      0.08      1.29   2825.15      1.00\n",
+      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  12007.14      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.67      1.47   3220.08      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3229.13      1.00\n",
+      " coefs[12]      0.10      0.65      0.09     -1.05      1.08   3214.88      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.99     -2.05     -0.06   5156.93      1.00\n",
+      " coefs[14]     -0.45      0.68     -0.35     -1.52      0.56   5786.49      1.00\n",
+      " coefs[15]     -0.76      0.58     -0.65     -1.65      0.08   4260.86      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.60      0.12   5213.66      1.00\n",
+      " coefs[17]     -0.04      0.17     -0.04     -0.31      0.23    558.39      1.00\n",
+      " coefs[18]     -0.52      0.68     -0.40     -1.59      0.44   6109.99      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.38     -1.58      0.58   5597.20      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5070.21      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.63      0.01   4634.14      1.00\n",
+      " coefs[22]      0.10      0.06      0.10      0.01      0.19    642.58      1.00\n",
+      " coefs[23]      0.12      0.24      0.11     -0.29      0.51    465.45      1.00\n",
+      " coefs[24]      0.09      0.15      0.09     -0.15      0.35    470.90      1.00\n",
+      " coefs[25]     -0.11      0.23     -0.11     -0.48      0.27    454.80      1.00\n",
+      " coefs[26]      0.00      0.18      0.00     -0.30      0.29    466.84      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   5204.11      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.60      1.66  11259.68      1.00\n",
+      " coefs[29]      0.09      0.08      0.08     -0.03      0.22    488.93      1.00\n",
+      " coefs[30]      0.02      0.09      0.03     -0.13      0.18    610.00      1.00\n",
+      " coefs[31]     -0.75      0.59     -0.63     -1.60      0.08   4911.00      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.05      0.23    463.51      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.06      0.37    460.50      1.00\n",
+      " coefs[34]      0.93      0.59      0.80      0.12      1.77   4713.75      1.00\n",
+      " coefs[35]      0.32      0.24      0.32     -0.07      0.72    450.32      1.00\n",
+      " coefs[36]      0.32      0.31      0.32     -0.19      0.82    446.76      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    449.21      1.00\n",
+      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.02   1126.07      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    542.39      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.12    514.96      1.00\n",
+      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1089.97      1.00\n",
+      " coefs[42]      0.05      0.41      0.05     -0.65      0.69    447.89      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.36      0.39    451.39      1.00\n",
+      " coefs[44]      0.18      0.21      0.18     -0.16      0.53    448.32      1.00\n",
+      " coefs[45]      0.12      0.30      0.12     -0.36      0.60    447.13      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.23      0.67    449.59      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.11     -0.25      0.03    961.34      1.00\n",
+      " coefs[48]     -0.10      0.06     -0.10     -0.20      0.00    482.43      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1292.54      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.73     -1.68     -0.06   5019.30      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.09     -0.36      0.19    453.50      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.14    453.09      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.37      0.05    458.05      1.00\n",
+      " coefs[54]     -1.69      0.19     -1.68     -2.00     -1.40   4062.23      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 05 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.98      0.06      1.98      1.88      2.08  10055.48      1.00\n",
+      "  coefs[1]     -0.09      0.03     -0.09     -0.15     -0.03  13343.50      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.06   3771.35      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.20   8377.00      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   9458.58      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  11099.64      1.00\n",
+      "  coefs[6]      0.16      0.28      0.16     -0.28      0.65   2986.01      1.00\n",
+      "  coefs[7]     -0.68      0.17     -0.67     -0.95     -0.39   3098.70      1.00\n",
+      "  coefs[8]      0.53      0.33      0.53      0.01      1.08   2974.13      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  12492.35      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.63      1.52   3281.51      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.05     -0.53      0.44   3280.68      1.00\n",
+      " coefs[12]      0.09      0.65      0.08     -0.95      1.20   3275.10      1.00\n",
+      " coefs[13]     -1.02      0.62     -0.96     -1.99      0.03   5048.16      1.00\n",
+      " coefs[14]     -0.45      0.66     -0.34     -1.48      0.55   6484.69      1.00\n",
+      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.07   4874.24      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.59     -1.60      0.13   5196.60      1.00\n",
+      " coefs[17]     -0.85      0.54     -0.75     -1.71     -0.04   4288.80      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.42   5984.25      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.52      0.61   6184.44      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.61      0.02   5183.95      1.00\n",
+      " coefs[21]     -0.76      0.60     -0.65     -1.61      0.06   5107.29      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    931.40      1.00\n",
+      " coefs[23]      0.12      0.25      0.12     -0.29      0.53    654.15      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    661.51      1.00\n",
+      " coefs[25]      0.02      0.24      0.02     -0.38      0.39    640.94      1.00\n",
+      " coefs[26]      0.08      0.18      0.08     -0.22      0.38    650.77      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   5054.07      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.60      1.71  12236.32      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    716.26      1.00\n",
+      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    819.35      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.63     -1.63      0.05   5197.70      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    664.44      1.00\n",
+      " coefs[33]      0.15      0.13      0.16     -0.07      0.37    636.44      1.00\n",
+      " coefs[34]      0.08      0.05      0.08      0.00      0.16    913.04      1.00\n",
+      " coefs[35]      0.38      0.25      0.38     -0.04      0.76    631.09      1.00\n",
+      " coefs[36]      0.41      0.32      0.42     -0.11      0.91    625.04      1.00\n",
+      " coefs[37]      0.16      0.20      0.17     -0.17      0.47    634.99      1.00\n",
+      " coefs[38]     -0.01      0.05     -0.01     -0.10      0.07   1734.43      1.00\n",
+      " coefs[39]      0.06      0.08      0.06     -0.07      0.18    733.19      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    751.19      1.00\n",
+      " coefs[41]     -0.77      0.58     -0.64     -1.64      0.04   5405.80      1.00\n",
+      " coefs[42]      0.13      0.42      0.13     -0.55      0.82    630.46      1.00\n",
+      " coefs[43]      0.06      0.24      0.07     -0.32      0.44    631.90      1.00\n",
+      " coefs[44]      0.19      0.22      0.19     -0.18      0.53    624.94      1.00\n",
+      " coefs[45]      0.17      0.30      0.17     -0.33      0.65    625.77      1.00\n",
+      " coefs[46]      0.25      0.28      0.25     -0.22      0.70    622.20      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.12     -0.25      0.03   1352.86      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    690.67      1.00\n",
+      " coefs[49]      0.01      0.03      0.01     -0.04      0.06   2201.81      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.07   4536.52      1.00\n",
+      " coefs[51]     -0.07      0.17     -0.07     -0.36      0.19    638.33      1.00\n",
+      " coefs[52]     -0.06      0.16     -0.05     -0.32      0.21    633.89      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.08    644.18      1.00\n",
+      " coefs[54]     -1.83      0.20     -1.82     -2.15     -1.50   4430.47      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 06 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.95      0.06      1.95      1.85      2.05  10029.37      1.00\n",
+      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02  12149.78      1.00\n",
+      "  coefs[2]     -0.07      0.07     -0.07     -0.18      0.04   3538.75      1.00\n",
+      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.23   7831.87      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.13     -0.02   8546.42      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  11509.36      1.00\n",
+      "  coefs[6]      0.22      0.26      0.21     -0.20      0.65   2659.06      1.00\n",
+      "  coefs[7]     -0.68      0.16     -0.68     -0.94     -0.42   2786.69      1.00\n",
+      "  coefs[8]      0.62      0.30      0.61      0.14      1.13   2692.12      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12142.73      1.00\n",
+      " coefs[10]      0.44      0.66      0.43     -0.66      1.52   3204.45      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.53      0.44   3207.91      1.00\n",
+      " coefs[12]      0.10      0.66      0.10     -1.00      1.17   3206.53      1.00\n",
+      " coefs[13]     -1.07      0.62     -1.02     -2.08     -0.09   4936.60      1.00\n",
+      " coefs[14]     -0.47      0.68     -0.35     -1.47      0.58   5590.17      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.08   4904.63      1.00\n",
+      " coefs[16]     -0.73      0.57     -0.62     -1.60      0.10   5217.49      1.00\n",
+      " coefs[17]      0.01      0.16      0.01     -0.25      0.27    685.60      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.43   5794.67      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.55      0.59   5598.62      1.00\n",
+      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4899.15      1.00\n",
+      " coefs[21]     -0.79      0.59     -0.66     -1.64      0.01   4949.36      1.00\n",
+      " coefs[22]      0.05      0.05      0.05     -0.04      0.14    761.87      1.00\n",
+      " coefs[23]      0.13      0.24      0.13     -0.25      0.54    591.47      1.00\n",
+      " coefs[24]      0.13      0.15      0.13     -0.11      0.38    583.33      1.00\n",
+      " coefs[25]     -0.16      0.23     -0.16     -0.54      0.21    579.37      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.30    591.59      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.60      0.16   5125.28      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.60      1.64  11076.76      1.00\n",
+      " coefs[29]     -0.03      0.09     -0.03     -0.17      0.10    762.71      1.00\n",
+      " coefs[30]      0.05      0.09      0.05     -0.09      0.20    775.29      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.11      0.13    865.56      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.20    593.73      1.00\n",
+      " coefs[33]      0.14      0.13      0.14     -0.08      0.35    568.23      1.00\n",
+      " coefs[34]      0.11      0.05      0.10      0.03      0.19    939.36      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.04      0.73    567.29      1.00\n",
+      " coefs[36]      0.33      0.31      0.33     -0.16      0.83    557.88      1.00\n",
+      " coefs[37]      0.18      0.19      0.18     -0.12      0.50    561.91      1.00\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.06    987.06      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    660.49      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    719.50      1.00\n",
+      " coefs[41]     -0.78      0.58     -0.66     -1.62      0.03   5507.11      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.66      0.66    565.26      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    572.24      1.00\n",
+      " coefs[44]      0.17      0.21      0.17     -0.19      0.49    559.31      1.00\n",
+      " coefs[45]      0.13      0.29      0.13     -0.35      0.61    560.67      1.00\n",
+      " coefs[46]      0.23      0.27      0.24     -0.22      0.67    565.95      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    932.54      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    626.56      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4698.19      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4890.12      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.11    581.16      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.37      0.13    576.92      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.07    586.00      1.00\n",
+      " coefs[54]     -1.69      0.18     -1.68     -1.98     -1.39   4293.06      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 07 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9250.39      1.00\n",
+      "  coefs[1]     -0.09      0.03     -0.09     -0.14     -0.03  11900.57      1.00\n",
+      "  coefs[2]     -0.07      0.06     -0.07     -0.18      0.03   3382.04      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.25   7273.45      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   8136.64      1.00\n",
+      "  coefs[5]     -0.08      0.03     -0.08     -0.14     -0.03  10454.22      1.00\n",
+      "  coefs[6]      0.18      0.25      0.17     -0.21      0.59   2678.54      1.00\n",
+      "  coefs[7]     -0.60      0.15     -0.60     -0.86     -0.37   2847.50      1.00\n",
+      "  coefs[8]      0.58      0.29      0.57      0.13      1.08   2654.20      1.00\n",
+      "  coefs[9]     -0.00      0.03     -0.00     -0.05      0.05  11135.80      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.64      1.49   2891.96      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.40   2908.39      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.96      1.18   2906.43      1.00\n",
+      " coefs[13]     -1.06      0.62     -1.00     -1.98      0.01   4513.52      1.00\n",
+      " coefs[14]     -0.45      0.68     -0.33     -1.50      0.58   5874.76      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.70     -1.69      0.00   4266.13      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.61     -1.61      0.10   5034.41      1.00\n",
+      " coefs[17]      0.03      0.17      0.03     -0.25      0.29    583.94      1.01\n",
+      " coefs[18]     -0.55      0.67     -0.42     -1.56      0.41   5785.31      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.36     -1.58      0.56   5403.98      1.00\n",
+      " coefs[20]     -0.76      0.58     -0.65     -1.60      0.04   5347.55      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1203.81      1.00\n",
+      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11    999.08      1.00\n",
+      " coefs[23]      0.18      0.25      0.19     -0.23      0.60    524.80      1.01\n",
+      " coefs[24]      0.08      0.16      0.08     -0.19      0.33    540.04      1.01\n",
+      " coefs[25]     -0.14      0.24     -0.14     -0.53      0.25    519.78      1.01\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.33      0.28    528.60      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.15   5063.80      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.60      1.66  10397.30      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    558.96      1.01\n",
+      " coefs[30]     -0.02      0.10     -0.02     -0.19      0.15    764.55      1.01\n",
+      " coefs[31]     -0.03      0.09     -0.03     -0.18      0.13   1073.59      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.10      0.20    533.20      1.01\n",
+      " coefs[33]      0.11      0.14      0.12     -0.10      0.34    521.92      1.01\n",
+      " coefs[34]      0.92      0.59      0.79      0.10      1.77   4646.56      1.00\n",
+      " coefs[35]      0.33      0.25      0.33     -0.08      0.73    510.92      1.01\n",
+      " coefs[36]      0.32      0.32      0.32     -0.22      0.83    510.46      1.01\n",
+      " coefs[37]      0.14      0.20      0.14     -0.21      0.45    510.92      1.01\n",
+      " coefs[38]     -0.07      0.05     -0.07     -0.15      0.01   1144.95      1.00\n",
+      " coefs[39]     -0.07      0.09     -0.07     -0.23      0.07    802.88      1.00\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    590.70      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.65      0.04   4782.36      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.66      0.74    511.47      1.01\n",
+      " coefs[43]     -0.01      0.24     -0.01     -0.41      0.37    519.40      1.01\n",
+      " coefs[44]      0.16      0.22      0.17     -0.22      0.50    513.40      1.01\n",
+      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    510.38      1.01\n",
+      " coefs[46]      0.21      0.29      0.22     -0.27      0.67    508.85      1.01\n",
+      " coefs[47]     -0.85      0.57     -0.73     -1.66     -0.05   4640.92      1.00\n",
+      " coefs[48]     -0.06      0.07     -0.06     -0.17      0.04    567.66      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.65     -0.00   4733.44      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4562.81      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.14     -0.42      0.15    524.03      1.01\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.33      0.21    517.19      1.01\n",
+      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.07    522.64      1.01\n",
+      " coefs[54]     -1.70      0.19     -1.69     -1.99     -1.39   3848.03      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 08 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.07      0.06      2.07      1.97      2.17   6006.90      1.00\n",
+      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02   6950.95      1.00\n",
+      "  coefs[2]     -0.02      0.07     -0.03     -0.15      0.10   2377.69      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   5572.29      1.00\n",
+      "  coefs[4]     -0.09      0.04     -0.09     -0.15     -0.03   5713.46      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.17     -0.22     -0.11   6679.18      1.00\n",
+      "  coefs[6]      0.41      0.30      0.40     -0.09      0.90   1949.82      1.00\n",
+      "  coefs[7]     -0.76      0.18     -0.75     -1.05     -0.45   2055.76      1.00\n",
+      "  coefs[8]      0.82      0.36      0.80      0.25      1.41   1971.61      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04   7249.79      1.00\n",
+      " coefs[10]      0.42      0.67      0.41     -0.62      1.57   2239.69      1.00\n",
+      " coefs[11]     -0.09      0.30     -0.10     -0.58      0.39   2251.76      1.00\n",
+      " coefs[12]      0.11      0.67      0.10     -0.95      1.24   2239.80      1.00\n",
+      " coefs[13]     -0.98      0.63     -0.92     -1.95      0.06   3243.72      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.53      0.52   3707.25      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.66      0.05   2946.07      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.61     -1.60      0.13   3752.58      1.00\n",
+      " coefs[17]     -0.13      0.19     -0.13     -0.46      0.16    896.44      1.01\n",
+      " coefs[18]     -0.55      0.67     -0.43     -1.56      0.44   4189.47      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.49      0.64   4551.92      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.64     -1.62      0.03   3922.11      1.00\n",
+      " coefs[21]     -0.76      0.59     -0.63     -1.61      0.05   3791.52      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.03      0.16    903.58      1.01\n",
+      " coefs[23]      0.10      0.25      0.10     -0.31      0.52    635.36      1.01\n",
+      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    629.98      1.01\n",
+      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    618.53      1.01\n",
+      " coefs[26]      0.01      0.18      0.01     -0.30      0.30    621.07      1.01\n",
+      " coefs[27]     -0.70      0.62     -0.57     -1.61      0.16   3618.38      1.00\n",
+      " coefs[28]     -0.77      0.60     -0.65     -1.61      0.03   3809.29      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    692.94      1.01\n",
+      " coefs[30]      0.11      0.09      0.11     -0.03      0.26    679.52      1.01\n",
+      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.07   3537.22      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    646.89      1.01\n",
+      " coefs[33]      0.19      0.13      0.19     -0.03      0.41    619.62      1.01\n",
+      " coefs[34]      0.10      0.05      0.10      0.01      0.18    970.71      1.00\n",
+      " coefs[35]      0.35      0.25      0.35     -0.04      0.77    606.18      1.01\n",
+      " coefs[36]      0.38      0.32      0.37     -0.14      0.90    604.82      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.14      0.51    610.69      1.01\n",
+      " coefs[38]     -0.77      0.57     -0.66     -1.58      0.02   3904.29      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    724.62      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    746.12      1.01\n",
+      " coefs[41]      0.04      0.06      0.04     -0.05      0.13    959.08      1.00\n",
+      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    605.63      1.01\n",
+      " coefs[43]      0.05      0.24      0.04     -0.33      0.44    609.63      1.01\n",
+      " coefs[44]      0.16      0.22      0.16     -0.20      0.52    605.83      1.01\n",
+      " coefs[45]      0.12      0.30      0.12     -0.40      0.60    602.34      1.01\n",
+      " coefs[46]      0.26      0.28      0.26     -0.21      0.72    603.36      1.01\n",
+      " coefs[47]     -0.08      0.07     -0.07     -0.19      0.04    976.89      1.00\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.23     -0.02    677.15      1.01\n",
+      " coefs[49]     -0.02      0.02     -0.02     -0.06      0.02   1377.67      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.71     -1.66     -0.07   3162.14      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.39      0.17    616.19      1.01\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.39      0.15    615.73      1.01\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.35      0.08    625.27      1.01\n",
+      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   2716.86      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 09 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.01      0.06      2.01      1.91      2.12   9583.20      1.00\n",
+      "  coefs[1]     -0.02      0.03     -0.02     -0.08      0.03  12244.17      1.00\n",
+      "  coefs[2]      0.00      0.07      0.00     -0.11      0.12   3899.89      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   7491.94      1.00\n",
+      "  coefs[4]     -0.06      0.03     -0.06     -0.11      0.00   8128.73      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  11573.08      1.00\n",
+      "  coefs[6]      0.41      0.27      0.41     -0.01      0.87   3193.36      1.00\n",
+      "  coefs[7]     -0.72      0.16     -0.72     -0.99     -0.46   3342.76      1.00\n",
+      "  coefs[8]      0.74      0.31      0.74      0.22      1.25   3174.21      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11291.83      1.00\n",
+      " coefs[10]      0.42      0.66      0.41     -0.66      1.50   3092.99      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.07     -0.55      0.41   3105.34      1.00\n",
+      " coefs[12]      0.08      0.66      0.07     -0.95      1.21   3098.35      1.00\n",
+      " coefs[13]     -0.98      0.63     -0.92     -2.01      0.04   4969.90      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.54      0.49   6361.60      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.66     -1.67      0.07   4862.64      1.00\n",
+      " coefs[16]     -0.69      0.58     -0.58     -1.56      0.15   5141.14      1.00\n",
+      " coefs[17]     -0.11      0.19     -0.10     -0.42      0.20    969.52      1.00\n",
+      " coefs[18]     -0.54      0.67     -0.42     -1.59      0.42   5803.27      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.52      0.60   5673.56      1.00\n",
+      " coefs[20]      0.01      0.97      0.01     -1.58      1.61  11893.53      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1600.17      1.00\n",
+      " coefs[22]      0.13      0.05      0.13      0.04      0.21    754.02      1.00\n",
+      " coefs[23]      0.07      0.25      0.08     -0.35      0.47    676.30      1.00\n",
+      " coefs[24]      0.05      0.16      0.06     -0.21      0.31    649.22      1.00\n",
+      " coefs[25]     -0.07      0.24     -0.07     -0.45      0.32    638.48      1.00\n",
+      " coefs[26]      0.04      0.18      0.05     -0.26      0.34    635.07      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.17   5073.59      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.61      1.64  10606.53      1.00\n",
+      " coefs[29]      0.07      0.08      0.08     -0.06      0.20    664.51      1.00\n",
+      " coefs[30]      0.02      0.10      0.02     -0.15      0.19    986.79      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.08   4279.14      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    654.63      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    644.38      1.00\n",
+      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4721.10      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.05      0.76    626.40      1.00\n",
+      " coefs[36]      0.32      0.32      0.33     -0.23      0.81    621.11      1.00\n",
+      " coefs[37]      0.17      0.20      0.18     -0.17      0.49    620.09      1.00\n",
+      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    942.45      1.00\n",
+      " coefs[39]      0.05      0.07      0.05     -0.08      0.17    701.99      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.04      0.13    756.89      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.63      0.06   5097.00      1.00\n",
+      " coefs[42]      0.03      0.42      0.04     -0.69      0.70    616.88      1.00\n",
+      " coefs[43]      0.00      0.24      0.01     -0.39      0.39    616.74      1.00\n",
+      " coefs[44]      0.18      0.22      0.18     -0.19      0.53    626.94      1.00\n",
+      " coefs[45]      0.13      0.30      0.14     -0.38      0.62    622.26      1.00\n",
+      " coefs[46]      0.23      0.28      0.23     -0.25      0.69    622.08      1.00\n",
+      " coefs[47]     -0.09      0.09     -0.09     -0.23      0.05   1262.87      1.00\n",
+      " coefs[48]     -0.05      0.06     -0.05     -0.15      0.05    672.90      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.66     -0.01   4912.08      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4527.27      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.39      0.17    629.31      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.13    621.60      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    630.94      1.00\n",
+      " coefs[54]     -1.72      0.19     -1.70     -2.04     -1.42   3986.73      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 10 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.87      0.06      1.87      1.77      1.97   9851.85      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  12023.27      1.00\n",
+      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.03   3664.70      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8152.42      1.00\n",
+      "  coefs[4]     -0.11      0.03     -0.11     -0.17     -0.05   9085.34      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11119.98      1.00\n",
+      "  coefs[6]      0.03      0.25      0.02     -0.38      0.44   2855.36      1.00\n",
+      "  coefs[7]     -0.55      0.15     -0.54     -0.80     -0.30   3027.65      1.00\n",
+      "  coefs[8]      0.36      0.29      0.36     -0.12      0.83   2848.40      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12091.31      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.70      1.43   3073.54      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.45   3091.90      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.96      1.17   3077.49      1.00\n",
+      " coefs[13]     -1.03      0.63     -0.97     -2.05     -0.03   5086.29      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.36     -1.52      0.54   5767.73      1.00\n",
+      " coefs[15]     -0.81      0.58     -0.70     -1.70      0.02   4429.92      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.62      0.10   5020.30      1.00\n",
+      " coefs[17]     -0.05      0.17     -0.05     -0.32      0.23    634.36      1.00\n",
+      " coefs[18]     -0.58      0.65     -0.47     -1.57      0.38   5653.50      1.00\n",
+      " coefs[19]     -0.49      0.68     -0.39     -1.57      0.56   5316.42      1.00\n",
+      " coefs[20]     -0.76      0.60     -0.64     -1.62      0.04   5141.74      1.00\n",
+      " coefs[21]      0.00      0.03      0.01     -0.04      0.06   1175.81      1.00\n",
+      " coefs[22]      0.09      0.05      0.09      0.00      0.17    589.10      1.00\n",
+      " coefs[23]      0.01      0.25      0.01     -0.39      0.42    537.95      1.00\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.29      0.23    562.57      1.00\n",
+      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.34    508.79      1.01\n",
+      " coefs[26]     -0.02      0.18     -0.02     -0.34      0.25    517.53      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.61      0.13   4770.04      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.55      1.72  10221.27      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.08      0.17    561.90      1.01\n",
+      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    748.10      1.00\n",
+      " coefs[31]     -0.01      0.08     -0.00     -0.13      0.12    783.81      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    532.06      1.01\n",
+      " coefs[33]      0.17      0.13      0.17     -0.06      0.37    514.16      1.01\n",
+      " coefs[34]      0.90      0.60      0.78      0.08      1.75   4699.27      1.00\n",
+      " coefs[35]      0.28      0.24      0.28     -0.10      0.69    505.90      1.01\n",
+      " coefs[36]      0.33      0.31      0.34     -0.17      0.84    505.30      1.01\n",
+      " coefs[37]      0.16      0.19      0.16     -0.16      0.47    503.53      1.01\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    827.64      1.00\n",
+      " coefs[39]     -0.03      0.08     -0.03     -0.16      0.11    663.60      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    666.94      1.00\n",
+      " coefs[41]     -0.81      0.59     -0.68     -1.71     -0.03   4477.38      1.00\n",
+      " coefs[42]      0.06      0.41      0.07     -0.61      0.73    504.16      1.01\n",
+      " coefs[43]      0.03      0.23      0.04     -0.35      0.41    506.87      1.01\n",
+      " coefs[44]      0.20      0.21      0.20     -0.14      0.55    502.28      1.01\n",
+      " coefs[45]      0.08      0.30      0.09     -0.40      0.57    503.49      1.01\n",
+      " coefs[46]      0.17      0.28      0.18     -0.29      0.62    501.86      1.01\n",
+      " coefs[47]     -0.09      0.07     -0.08     -0.20      0.03    751.62      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    553.11      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.01   4806.02      1.00\n",
+      " coefs[50]     -0.83      0.59     -0.70     -1.67     -0.03   4711.38      1.00\n",
+      " coefs[51]     -0.08      0.17     -0.08     -0.36      0.18    505.60      1.01\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.32      0.19    510.68      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.01    515.18      1.01\n",
+      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.33   4089.82      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 11 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.92      0.06      1.92      1.82      2.02  10396.90      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.03  11519.16      1.00\n",
+      "  coefs[2]     -0.06      0.06     -0.06     -0.16      0.04   4117.58      1.00\n",
+      "  coefs[3]     -0.29      0.03     -0.29     -0.35     -0.23   7737.34      1.00\n",
+      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8773.20      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.18     -0.22     -0.12  11016.25      1.00\n",
+      "  coefs[6]      0.19      0.21      0.18     -0.16      0.50   2829.57      1.00\n",
+      "  coefs[7]     -0.59      0.13     -0.58     -0.79     -0.38   3123.90      1.00\n",
+      "  coefs[8]      0.48      0.24      0.46      0.09      0.85   2830.52      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.09      0.00  12268.23      1.00\n",
+      " coefs[10]      0.45      0.66      0.44     -0.64      1.53   3044.65      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.40   3052.36      1.00\n",
+      " coefs[12]      0.08      0.65      0.07     -1.01      1.15   3041.06      1.00\n",
+      " coefs[13]     -1.03      0.62     -0.97     -2.08     -0.06   4562.95      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.35     -1.55      0.51   5903.18      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.70     -1.67      0.02   4665.74      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.63      0.10   4957.23      1.00\n",
+      " coefs[17]      0.00      0.17      0.00     -0.27      0.28    610.13      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.41   5781.93      1.00\n",
+      " coefs[19]     -0.46      0.67     -0.37     -1.56      0.55   6074.50      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.03   5252.85      1.00\n",
+      " coefs[21]     -0.00      0.03     -0.00     -0.05      0.05   1165.34      1.00\n",
+      " coefs[22]      0.05      0.05      0.06     -0.04      0.14    680.97      1.00\n",
+      " coefs[23]      0.09      0.25      0.10     -0.34      0.48    529.12      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.01     -0.27      0.25    558.96      1.00\n",
+      " coefs[25]     -0.03      0.23     -0.02     -0.43      0.35    525.19      1.00\n",
+      " coefs[26]      0.06      0.18      0.07     -0.23      0.36    518.36      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.62      0.13   4954.67      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.61      1.65  10846.53      1.00\n",
+      " coefs[29]      0.05      0.08      0.06     -0.08      0.18    563.62      1.00\n",
+      " coefs[30]     -0.05      0.10     -0.04     -0.22      0.11    807.13      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.65     -1.62      0.03   4982.14      1.00\n",
+      " coefs[32]      0.09      0.09      0.10     -0.06      0.24    543.12      1.00\n",
+      " coefs[33]      0.14      0.13      0.14     -0.08      0.36    525.64      1.00\n",
+      " coefs[34]      0.16      0.06      0.15      0.06      0.26   1251.32      1.00\n",
+      " coefs[35]      0.38      0.25      0.39     -0.01      0.81    516.49      1.00\n",
+      " coefs[36]      0.34      0.31      0.35     -0.19      0.85    511.53      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.14      0.51    514.24      1.00\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.05    703.70      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    596.82      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.15    671.03      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   4996.10      1.00\n",
+      " coefs[42]      0.08      0.42      0.09     -0.63      0.76    512.64      1.00\n",
+      " coefs[43]      0.00      0.23      0.01     -0.38      0.40    516.39      1.00\n",
+      " coefs[44]      0.18      0.22      0.18     -0.18      0.53    514.45      1.00\n",
+      " coefs[45]      0.15      0.30      0.16     -0.35      0.64    513.91      1.00\n",
+      " coefs[46]      0.23      0.28      0.24     -0.24      0.69    514.26      1.00\n",
+      " coefs[47]     -0.85      0.57     -0.72     -1.67     -0.04   4633.11      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    600.11      1.00\n",
+      " coefs[49]     -0.80      0.60     -0.68     -1.64      0.00   4628.84      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.09   4617.98      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.09     -0.40      0.17    524.69      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.40      0.14    525.01      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.09    532.74      1.00\n",
+      " coefs[54]     -1.74      0.19     -1.73     -2.04     -1.43   3929.35      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 12 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.93      2.14   8304.52      1.00\n",
+      "  coefs[1]     -0.01      0.04     -0.01     -0.06      0.06  10118.62      1.00\n",
+      "  coefs[2]     -0.12      0.07     -0.11     -0.24     -0.00   3682.19      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   6963.70      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.15     -0.04   7744.04      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.09  10497.57      1.00\n",
+      "  coefs[6]      0.11      0.28      0.11     -0.34      0.58   2964.29      1.00\n",
+      "  coefs[7]     -0.58      0.17     -0.58     -0.85     -0.29   3083.36      1.00\n",
+      "  coefs[8]      0.40      0.33      0.39     -0.15      0.92   2948.26      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  10148.21      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.72      1.41   3238.54      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3251.02      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -0.94      1.19   3237.31      1.00\n",
+      " coefs[13]     -1.00      0.63     -0.94     -2.09     -0.05   4687.49      1.00\n",
+      " coefs[14]     -0.44      0.67     -0.34     -1.50      0.56   6099.61      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.07   4550.37      1.00\n",
+      " coefs[16]     -0.71      0.58     -0.60     -1.61      0.12   4864.50      1.00\n",
+      " coefs[17]     -0.13      0.19     -0.12     -0.45      0.19    940.69      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.43     -1.56      0.40   5805.63      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.59      0.55   5277.45      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   4861.90      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5058.03      1.00\n",
+      " coefs[22]      0.10      0.05      0.10      0.02      0.19    791.84      1.00\n",
+      " coefs[23]      0.10      0.25      0.10     -0.30      0.52    650.30      1.00\n",
+      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    644.67      1.00\n",
+      " coefs[25]     -0.01      0.24     -0.00     -0.39      0.38    630.09      1.00\n",
+      " coefs[26]      0.11      0.18      0.12     -0.17      0.43    635.35      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.63      0.14   4712.25      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.60      1.67  10040.11      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.07      0.18    679.39      1.00\n",
+      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    786.03      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.63      0.06   5149.75      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.06      0.24    650.45      1.00\n",
+      " coefs[33]      0.13      0.14      0.13     -0.07      0.37    630.38      1.00\n",
+      " coefs[34]      0.14      0.06      0.13      0.03      0.24   1370.58      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.04      0.78    620.21      1.00\n",
+      " coefs[36]      0.36      0.32      0.36     -0.16      0.89    619.37      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.15      0.51    624.44      1.00\n",
+      " coefs[38]     -0.04      0.05     -0.03     -0.11      0.04   1296.38      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    734.11      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    758.44      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   5148.08      1.00\n",
+      " coefs[42]      0.12      0.43      0.13     -0.57      0.81    620.28      1.00\n",
+      " coefs[43]      0.03      0.24      0.03     -0.36      0.41    626.67      1.00\n",
+      " coefs[44]      0.15      0.22      0.16     -0.20      0.52    626.95      1.00\n",
+      " coefs[45]      0.10      0.31      0.11     -0.38      0.61    624.04      1.00\n",
+      " coefs[46]      0.22      0.29      0.23     -0.24      0.70    618.56      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    994.64      1.00\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.01    668.23      1.00\n",
+      " coefs[49]     -0.79      0.59     -0.68     -1.64      0.00   4915.15      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.71     -1.69     -0.05   4731.62      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.20    629.43      1.00\n",
+      " coefs[52]     -0.05      0.16     -0.04     -0.31      0.22    625.15      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.13     -0.35      0.08    645.94      1.00\n",
+      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.42   3867.53      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 13 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.06      0.06      2.06      1.96      2.16  10107.97      1.00\n",
+      "  coefs[1]     -0.07      0.04     -0.07     -0.12     -0.01  12223.43      1.00\n",
+      "  coefs[2]     -0.21      0.07     -0.21     -0.33     -0.08   3247.79      1.00\n",
+      "  coefs[3]     -0.34      0.03     -0.34     -0.40     -0.28   7744.39      1.00\n",
+      "  coefs[4]     -0.11      0.04     -0.11     -0.17     -0.05   8886.81      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  10594.79      1.00\n",
+      "  coefs[6]     -0.08      0.30     -0.08     -0.56      0.41   2710.82      1.00\n",
+      "  coefs[7]     -0.52      0.18     -0.52     -0.82     -0.23   2838.19      1.00\n",
+      "  coefs[8]      0.17      0.35      0.17     -0.39      0.74   2697.80      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.02  11093.40      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.67      1.48   3051.80      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.52      0.43   3043.81      1.00\n",
+      " coefs[12]      0.06      0.65      0.06     -1.06      1.08   3055.42      1.00\n",
+      " coefs[13]     -0.91      0.65     -0.86     -1.95      0.15   4747.74      1.00\n",
+      " coefs[14]     -0.48      0.66     -0.37     -1.53      0.49   5540.97      1.00\n",
+      " coefs[15]     -0.77      0.56     -0.67     -1.63      0.05   4870.06      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.59      0.14   4957.56      1.00\n",
+      " coefs[17]     -0.06      0.18     -0.05     -0.34      0.23    543.36      1.01\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.40   5806.90      1.00\n",
+      " coefs[19]     -0.49      0.67     -0.39     -1.56      0.58   5841.70      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5195.52      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.05      0.06   1082.76      1.00\n",
+      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    592.12      1.01\n",
+      " coefs[23]     -0.10      0.26     -0.10     -0.52      0.32    461.09      1.01\n",
+      " coefs[24]      0.00      0.16      0.00     -0.26      0.26    453.93      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.44      0.32    426.89      1.01\n",
+      " coefs[26]      0.06      0.18      0.06     -0.25      0.35    434.65      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.14   5038.79      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.69      1.60  11808.60      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.10      0.16    486.47      1.01\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.31      0.10   1023.19      1.01\n",
+      " coefs[31]      0.02      0.08      0.02     -0.11      0.15    677.56      1.01\n",
+      " coefs[32]      0.07      0.09      0.08     -0.07      0.22    442.33      1.01\n",
+      " coefs[33]      0.13      0.13      0.14     -0.08      0.35    431.07      1.01\n",
+      " coefs[34]      0.91      0.60      0.79      0.11      1.80   5008.02      1.00\n",
+      " coefs[35]      0.31      0.25      0.31     -0.09      0.70    419.67      1.01\n",
+      " coefs[36]      0.32      0.31      0.32     -0.21      0.81    421.90      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.15      0.49    426.28      1.01\n",
+      " coefs[38]     -0.06      0.05     -0.05     -0.13      0.02   1113.26      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    480.00      1.01\n",
+      " coefs[40]      0.10      0.05      0.10      0.02      0.19    500.83      1.01\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1035.85      1.01\n",
+      " coefs[42]     -0.00      0.42      0.00     -0.70      0.67    423.22      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.40      0.36    427.20      1.01\n",
+      " coefs[44]      0.18      0.22      0.18     -0.17      0.53    421.49      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.42      0.56    416.39      1.01\n",
+      " coefs[46]      0.22      0.28      0.22     -0.25      0.66    423.39      1.01\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.06    637.28      1.01\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    457.03      1.01\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.00   4772.50      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.75     -1.69     -0.07   4318.31      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.13    423.95      1.01\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.13    434.85      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.19     -0.40      0.02    437.62      1.01\n",
+      " coefs[54]     -1.71      0.19     -1.69     -2.01     -1.41   4099.94      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 14 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.08   9005.66      1.00\n",
+      "  coefs[1]     -0.02      0.03     -0.02     -0.07      0.04  11557.78      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.16      0.05   4138.63      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7839.59      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8500.08      1.00\n",
+      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  10663.93      1.00\n",
+      "  coefs[6]      0.14      0.25      0.13     -0.25      0.55   3159.51      1.00\n",
+      "  coefs[7]     -0.61      0.15     -0.60     -0.85     -0.36   3309.15      1.00\n",
+      "  coefs[8]      0.47      0.29      0.46     -0.03      0.91   3123.20      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.05  11937.39      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.71      1.44   3091.25      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.57      0.39   3085.88      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -1.03      1.11   3094.82      1.00\n",
+      " coefs[13]     -1.02      0.63     -0.96     -2.08     -0.04   5050.19      1.00\n",
+      " coefs[14]     -0.47      0.68     -0.36     -1.53      0.53   5346.83      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.64      0.05   4722.58      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.62      0.11   4855.77      1.00\n",
+      " coefs[17]     -0.03      0.18     -0.03     -0.31      0.27    720.50      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.43   6038.97      1.00\n",
+      " coefs[19]     -0.47      0.69     -0.38     -1.51      0.66   5416.81      1.00\n",
+      " coefs[20]      0.02      0.98      0.01     -1.59      1.63  13208.44      1.00\n",
+      " coefs[21]      0.02      0.99      0.02     -1.54      1.70  10823.00      1.00\n",
+      " coefs[22]     -0.02      0.07     -0.01     -0.13      0.10   1087.05      1.00\n",
+      " coefs[23]      0.05      0.25      0.05     -0.36      0.48    562.53      1.00\n",
+      " coefs[24]     -0.06      0.17     -0.06     -0.34      0.21    601.03      1.00\n",
+      " coefs[25]     -0.06      0.24     -0.05     -0.46      0.34    550.41      1.00\n",
+      " coefs[26]      0.07      0.19      0.07     -0.23      0.38    546.27      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.15   4953.64      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.57      1.67  10744.99      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    590.76      1.00\n",
+      " coefs[30]      0.02      0.10      0.03     -0.14      0.18    710.84      1.00\n",
+      " coefs[31]     -0.78      0.58     -0.66     -1.62      0.05   5056.04      1.00\n",
+      " coefs[32]      0.04      0.09      0.04     -0.11      0.20    568.43      1.00\n",
+      " coefs[33]      0.15      0.14      0.15     -0.06      0.39    546.49      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.11      1.78   4921.83      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.08      0.74    542.19      1.00\n",
+      " coefs[36]      0.33      0.32      0.33     -0.19      0.88    538.22      1.00\n",
+      " coefs[37]      0.13      0.20      0.13     -0.19      0.48    539.85      1.00\n",
+      " coefs[38]      0.02      0.04      0.02     -0.05      0.10   1055.60      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    606.11      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    634.23      1.00\n",
+      " coefs[41]      0.02      0.06      0.03     -0.07      0.12    852.14      1.00\n",
+      " coefs[42]      0.07      0.43      0.08     -0.65      0.77    540.64      1.00\n",
+      " coefs[43]     -0.04      0.24     -0.04     -0.44      0.35    546.56      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.19      0.53    536.30      1.00\n",
+      " coefs[45]      0.11      0.31      0.11     -0.39      0.64    535.15      1.00\n",
+      " coefs[46]      0.18      0.29      0.18     -0.30      0.65    540.24      1.00\n",
+      " coefs[47]     -0.02      0.06     -0.01     -0.12      0.09    669.38      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.03    578.06      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.02   4966.31      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.71     -1.69     -0.06   5157.37      1.00\n",
+      " coefs[51]     -0.05      0.18     -0.04     -0.34      0.24    549.11      1.00\n",
+      " coefs[52]     -0.13      0.17     -0.13     -0.41      0.13    546.42      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.39      0.05    554.62      1.00\n",
+      " coefs[54]     -1.64      0.19     -1.63     -1.95     -1.34   4052.25      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 15 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.05      0.06      2.05      1.94      2.14   9177.00      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.00  11743.81      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.02   3628.73      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.38     -0.27   7842.18      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8649.39      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  10859.96      1.00\n",
+      "  coefs[6]      0.37      0.27      0.36     -0.08      0.79   2752.83      1.00\n",
+      "  coefs[7]     -0.83      0.16     -0.83     -1.09     -0.56   2920.83      1.00\n",
+      "  coefs[8]      0.83      0.31      0.82      0.31      1.33   2750.68      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11841.94      1.00\n",
+      " coefs[10]      0.40      0.65      0.39     -0.70      1.44   3135.56      1.00\n",
+      " coefs[11]     -0.01      0.29     -0.02     -0.49      0.47   3135.50      1.00\n",
+      " coefs[12]      0.15      0.65      0.14     -0.89      1.24   3127.87      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.01     -2.06     -0.10   5383.26      1.00\n",
+      " coefs[14]     -0.45      0.66     -0.34     -1.47      0.56   5506.65      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.68     -1.68      0.01   4585.23      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.59      0.12   5284.94      1.00\n",
+      " coefs[17]     -0.27      0.22     -0.26     -0.63      0.09   1153.36      1.00\n",
+      " coefs[18]     -0.52      0.67     -0.41     -1.54      0.47   5888.75      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.36     -1.55      0.63   6200.15      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   4811.83      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.67     -1.64      0.01   4300.73      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.04      0.15    790.42      1.01\n",
+      " coefs[23]      0.22      0.24      0.21     -0.16      0.62    521.03      1.01\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.28      0.23    561.51      1.01\n",
+      " coefs[25]     -0.05      0.23     -0.05     -0.42      0.32    512.26      1.01\n",
+      " coefs[26]      0.00      0.18      0.00     -0.28      0.29    515.81      1.01\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.13   5153.89      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.60      1.67  11091.19      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.12      0.14    604.99      1.01\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.29      0.12   1242.60      1.00\n",
+      " coefs[31]      0.04      0.07      0.04     -0.09      0.15    737.77      1.01\n",
+      " coefs[32]      0.05      0.09      0.05     -0.09      0.19    527.77      1.01\n",
+      " coefs[33]      0.14      0.13      0.14     -0.06      0.35    518.80      1.01\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.76   4699.77      1.00\n",
+      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    503.71      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.20      0.79    506.01      1.01\n",
+      " coefs[37]      0.10      0.19      0.10     -0.22      0.41    509.89      1.01\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    903.45      1.01\n",
+      " coefs[39]      0.05      0.07      0.05     -0.06      0.17    542.48      1.01\n",
+      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    655.54      1.01\n",
+      " coefs[41]      0.02      0.05      0.02     -0.07      0.10    905.27      1.01\n",
+      " coefs[42]      0.04      0.41      0.04     -0.61      0.71    503.61      1.01\n",
+      " coefs[43]     -0.00      0.23     -0.00     -0.37      0.37    512.92      1.01\n",
+      " coefs[44]      0.16      0.21      0.15     -0.17      0.51    504.57      1.01\n",
+      " coefs[45]      0.07      0.29      0.07     -0.40      0.55    502.69      1.01\n",
+      " coefs[46]      0.18      0.27      0.18     -0.25      0.64    506.09      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.18      0.04    782.66      1.01\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    544.83      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.63      0.02   4838.35      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.75     -1.69     -0.08   4164.47      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.36      0.18    515.73      1.01\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.13    507.39      1.01\n",
+      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.01    515.72      1.01\n",
+      " coefs[54]     -1.66      0.18     -1.64     -1.96     -1.36   4343.76      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 16 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9179.36      1.00\n",
+      "  coefs[1]      0.01      0.03      0.01     -0.05      0.07  10791.72      1.00\n",
+      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3510.14      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   7615.67      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8998.44      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10867.82      1.00\n",
+      "  coefs[6]      0.50      0.29      0.49      0.02      0.99   2920.24      1.00\n",
+      "  coefs[7]     -0.79      0.18     -0.79     -1.08     -0.48   3039.41      1.00\n",
+      "  coefs[8]      0.87      0.35      0.86      0.27      1.42   2922.72      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11173.31      1.00\n",
+      " coefs[10]      0.46      0.65      0.45     -0.57      1.54   3308.73      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.43   3324.22      1.00\n",
+      " coefs[12]      0.08      0.65      0.08     -0.96      1.14   3310.11      1.00\n",
+      " coefs[13]     -1.05      0.62     -0.99     -2.00     -0.03   4531.52      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.51      0.52   5577.25      1.00\n",
+      " coefs[15]     -0.78      0.58     -0.68     -1.64      0.08   4391.98      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.57      0.15   4813.23      1.00\n",
+      " coefs[17]     -0.29      0.22     -0.28     -0.65      0.08   1050.49      1.00\n",
+      " coefs[18]     -0.55      0.67     -0.43     -1.57      0.42   5579.16      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.60      0.54   5415.16      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5013.34      1.00\n",
+      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.03   4630.94      1.00\n",
+      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    831.29      1.00\n",
+      " coefs[23]      0.12      0.24      0.12     -0.28      0.51    565.03      1.01\n",
+      " coefs[24]      0.10      0.15      0.11     -0.14      0.36    566.50      1.01\n",
+      " coefs[25]     -0.06      0.23     -0.06     -0.44      0.31    544.78      1.01\n",
+      " coefs[26]      0.04      0.18      0.04     -0.25      0.33    556.89      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   4905.08      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.69  10411.65      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    596.47      1.01\n",
+      " coefs[30]      0.04      0.09      0.04     -0.11      0.18    684.25      1.00\n",
+      " coefs[31]      0.04      0.07      0.04     -0.07      0.15    717.08      1.01\n",
+      " coefs[32]      0.09      0.09      0.10     -0.06      0.23    560.88      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.06      0.36    550.32      1.01\n",
+      " coefs[34]      0.90      0.60      0.79      0.09      1.79   4522.53      1.00\n",
+      " coefs[35]      0.33      0.24      0.33     -0.06      0.72    542.54      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.19      0.81    538.21      1.01\n",
+      " coefs[37]      0.17      0.19      0.18     -0.16      0.47    545.27      1.01\n",
+      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    873.71      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.15    679.04      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.05      0.10    628.08      1.01\n",
+      " coefs[41]     -0.80      0.59     -0.67     -1.67      0.03   4771.75      1.00\n",
+      " coefs[42]      0.02      0.41      0.03     -0.65      0.68    537.69      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.38      0.36    545.99      1.01\n",
+      " coefs[44]      0.19      0.21      0.19     -0.18      0.51    539.59      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.41      0.55    540.83      1.01\n",
+      " coefs[46]      0.22      0.28      0.23     -0.23      0.66    538.97      1.01\n",
+      " coefs[47]     -0.02      0.07     -0.02     -0.13      0.09    789.16      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.04    598.54      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.65      0.02   4719.61      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.70     -0.07   4374.23      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    547.36      1.01\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.16    550.52      1.01\n",
+      " coefs[53]     -0.12      0.13     -0.12     -0.33      0.08    546.83      1.01\n",
+      " coefs[54]     -1.68      0.18     -1.67     -1.98     -1.38   3683.28      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 17 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.12   9825.76      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.01  11491.29      1.00\n",
+      "  coefs[2]     -0.12      0.07     -0.12     -0.24     -0.02   4035.17      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7508.58      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8850.54      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  10832.36      1.00\n",
+      "  coefs[6]     -0.03      0.25     -0.03     -0.43      0.39   3103.03      1.00\n",
+      "  coefs[7]     -0.49      0.15     -0.49     -0.74     -0.24   3302.29      1.00\n",
+      "  coefs[8]      0.26      0.29      0.26     -0.20      0.74   3075.37      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.12     -0.03  11096.54      1.00\n",
+      " coefs[10]      0.47      0.64      0.47     -0.61      1.49   3268.81      1.00\n",
+      " coefs[11]     -0.08      0.29     -0.08     -0.59      0.35   3299.38      1.00\n",
+      " coefs[12]      0.07      0.64      0.06     -1.04      1.07   3296.69      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.07     -0.09   4800.78      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.52   5846.17      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.69     -1.62      0.06   4206.97      1.00\n",
+      " coefs[16]     -0.71      0.58     -0.60     -1.58      0.14   5088.30      1.00\n",
+      " coefs[17]     -0.05      0.18     -0.05     -0.33      0.24    599.68      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.45   5927.75      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.58   5998.88      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.67     -1.62      0.01   4825.52      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1133.37      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    589.43      1.01\n",
+      " coefs[23]      0.15      0.25      0.15     -0.26      0.56    468.13      1.01\n",
+      " coefs[24]      0.13      0.16      0.13     -0.14      0.37    471.51      1.01\n",
+      " coefs[25]     -0.03      0.23     -0.03     -0.41      0.36    459.24      1.01\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    473.85      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.62      0.14   4955.11      1.00\n",
+      " coefs[28]      0.01      0.99      0.01     -1.53      1.73  10769.97      1.00\n",
+      " coefs[29]     -0.00      0.08     -0.01     -0.13      0.13    522.04      1.01\n",
+      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    527.10      1.01\n",
+      " coefs[31]      0.04      0.07      0.04     -0.08      0.16    648.90      1.01\n",
+      " coefs[32]      0.10      0.09      0.10     -0.04      0.25    479.99      1.01\n",
+      " coefs[33]      0.12      0.13      0.12     -0.10      0.34    472.55      1.01\n",
+      " coefs[34]      0.11      0.05      0.11      0.03      0.20    757.54      1.01\n",
+      " coefs[35]      0.29      0.25      0.29     -0.10      0.70    452.91      1.01\n",
+      " coefs[36]      0.34      0.31      0.34     -0.21      0.83    453.74      1.01\n",
+      " coefs[37]      0.16      0.20      0.16     -0.17      0.48    458.11      1.01\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    759.34      1.01\n",
+      " coefs[39]     -0.03      0.08     -0.03     -0.17      0.10    622.87      1.01\n",
+      " coefs[40]      0.08      0.05      0.08     -0.00      0.17    627.81      1.01\n",
+      " coefs[41]     -0.78      0.60     -0.66     -1.68      0.02   5038.60      1.00\n",
+      " coefs[42]     -0.02      0.42     -0.02     -0.68      0.70    454.27      1.01\n",
+      " coefs[43]     -0.05      0.23     -0.05     -0.44      0.33    462.64      1.01\n",
+      " coefs[44]      0.19      0.22      0.18     -0.17      0.54    455.92      1.01\n",
+      " coefs[45]      0.11      0.30      0.11     -0.40      0.59    455.52      1.01\n",
+      " coefs[46]      0.20      0.28      0.20     -0.28      0.64    452.79      1.01\n",
+      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    647.18      1.01\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.02    503.96      1.01\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.66     -0.01   4790.18      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.73     -1.69     -0.06   4353.25      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.16    465.74      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.39      0.14    460.95      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    466.41      1.01\n",
+      " coefs[54]     -1.69      0.18     -1.67     -1.97     -1.38   4247.42      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 18 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.01      0.06      2.01      1.91      2.11   9222.07      1.00\n",
+      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.02  11037.73      1.00\n",
+      "  coefs[2]     -0.11      0.06     -0.11     -0.22     -0.01   3896.77      1.00\n",
+      "  coefs[3]     -0.38      0.03     -0.38     -0.44     -0.33   7697.55      1.00\n",
+      "  coefs[4]     -0.04      0.03     -0.05     -0.10      0.01   8703.86      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10405.15      1.00\n",
+      "  coefs[6]      0.12      0.23      0.12     -0.24      0.51   2968.23      1.00\n",
+      "  coefs[7]     -0.60      0.14     -0.60     -0.83     -0.36   3184.79      1.00\n",
+      "  coefs[8]      0.42      0.27      0.42     -0.02      0.86   2967.49      1.00\n",
+      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  11147.01      1.00\n",
+      " coefs[10]      0.44      0.65      0.44     -0.67      1.48   2962.23      1.00\n",
+      " coefs[11]     -0.08      0.29     -0.08     -0.56      0.40   2974.48      1.00\n",
+      " coefs[12]      0.07      0.65      0.07     -1.00      1.15   2969.88      1.00\n",
+      " coefs[13]     -0.99      0.64     -0.93     -2.05      0.01   4667.16      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.52   5983.57      1.00\n",
+      " coefs[15]     -0.78      0.58     -0.67     -1.66      0.06   4759.51      1.00\n",
+      " coefs[16]     -0.70      0.58     -0.60     -1.57      0.13   5111.37      1.00\n",
+      " coefs[17]     -0.02      0.17     -0.02     -0.30      0.25    723.30      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   5519.08      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.58      0.55   5869.82      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.67     -1.63      0.01   4721.83      1.00\n",
+      " coefs[21]     -0.77      0.58     -0.66     -1.60      0.03   5203.05      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    742.09      1.01\n",
+      " coefs[23]      0.05      0.25      0.05     -0.36      0.45    635.21      1.01\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.30      0.22    658.36      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.30    612.30      1.01\n",
+      " coefs[26]      0.04      0.18      0.05     -0.26      0.33    624.90      1.01\n",
+      " coefs[27]     -0.70      0.62     -0.58     -1.60      0.17   5010.88      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.62      1.66  10001.87      1.00\n",
+      " coefs[29]      0.03      0.08      0.03     -0.11      0.15    670.66      1.01\n",
+      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    741.75      1.01\n",
+      " coefs[31]     -0.00      0.08     -0.00     -0.13      0.12    871.75      1.01\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    641.81      1.01\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    606.63      1.01\n",
+      " coefs[34]      0.15      0.06      0.14      0.05      0.25   1321.74      1.00\n",
+      " coefs[35]      0.33      0.24      0.33     -0.08      0.71    602.00      1.01\n",
+      " coefs[36]      0.33      0.31      0.33     -0.17      0.84    599.72      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.14      0.50    607.37      1.01\n",
+      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    825.58      1.01\n",
+      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    688.22      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    737.72      1.01\n",
+      " coefs[41]      0.01      0.07      0.02     -0.10      0.12   1492.59      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.68      0.69    602.54      1.01\n",
+      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.34    613.82      1.01\n",
+      " coefs[44]      0.19      0.21      0.19     -0.16      0.54    604.50      1.01\n",
+      " coefs[45]      0.13      0.30      0.14     -0.39      0.59    603.75      1.01\n",
+      " coefs[46]      0.23      0.28      0.23     -0.23      0.68    609.11      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.06     -0.18      0.05    933.07      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    672.42      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.65      0.00   4630.65      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4276.88      1.00\n",
+      " coefs[51]     -0.07      0.17     -0.07     -0.35      0.21    624.71      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.12    615.24      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    608.75      1.01\n",
+      " coefs[54]     -1.65      0.19     -1.64     -1.94     -1.35   3844.77      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 19 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.09      0.06      2.09      1.99      2.20   9900.43      1.00\n",
+      "  coefs[1]     -0.09      0.04     -0.09     -0.15     -0.03  12225.38      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3777.37      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   8256.62      1.00\n",
+      "  coefs[4]     -0.13      0.04     -0.13     -0.18     -0.07   9095.25      1.00\n",
+      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  11139.58      1.00\n",
+      "  coefs[6]      0.43      0.28      0.42     -0.03      0.90   3032.91      1.00\n",
+      "  coefs[7]     -0.85      0.17     -0.84     -1.13     -0.56   3189.63      1.00\n",
+      "  coefs[8]      0.87      0.33      0.86      0.30      1.40   3022.08      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  12442.31      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.72      1.41   3331.08      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.07     -0.54      0.41   3341.18      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -1.03      1.10   3333.96      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.01     -2.05     -0.08   5218.74      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.54      0.52   5822.97      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.65      0.06   4591.28      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.61     -1.62      0.14   5379.81      1.00\n",
+      " coefs[17]      0.00      0.17      0.01     -0.26      0.29    769.45      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   6037.22      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.36     -1.52      0.62   6056.28      1.00\n",
+      " coefs[20]     -0.77      0.60     -0.65     -1.63      0.03   4989.46      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1593.75      1.00\n",
+      " coefs[22]      0.09      0.05      0.10      0.01      0.18    737.03      1.00\n",
+      " coefs[23]      0.20      0.25      0.21     -0.21      0.61    633.08      1.00\n",
+      " coefs[24]      0.08      0.16      0.09     -0.17      0.34    632.23      1.00\n",
+      " coefs[25]     -0.10      0.24     -0.10     -0.46      0.31    630.33      1.00\n",
+      " coefs[26]      0.08      0.18      0.08     -0.21      0.39    615.33      1.00\n",
+      " coefs[27]     -0.67      0.63     -0.55     -1.59      0.22   5405.23      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.67      1.63  11841.95      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.13      0.13    726.36      1.00\n",
+      " coefs[30]      0.10      0.09      0.10     -0.05      0.23    715.32      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1298.58      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    653.45      1.00\n",
+      " coefs[33]      0.11      0.13      0.11     -0.12      0.32    620.44      1.00\n",
+      " coefs[34]      0.93      0.59      0.82      0.12      1.77   4759.24      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.04      0.76    611.41      1.00\n",
+      " coefs[36]      0.34      0.31      0.35     -0.18      0.84    609.07      1.00\n",
+      " coefs[37]      0.18      0.20      0.18     -0.16      0.49    617.89      1.00\n",
+      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    798.81      1.00\n",
+      " coefs[39]     -0.05      0.09     -0.05     -0.20      0.09    945.47      1.00\n",
+      " coefs[40]      0.08      0.05      0.08     -0.00      0.16    775.94      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.68      0.02   5087.86      1.00\n",
+      " coefs[42]      0.02      0.42      0.03     -0.65      0.71    610.24      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.36      0.40    613.65      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.19      0.52    615.17      1.00\n",
+      " coefs[45]      0.04      0.30      0.05     -0.46      0.52    611.35      1.00\n",
+      " coefs[46]      0.18      0.28      0.19     -0.27      0.65    618.14      1.00\n",
+      " coefs[47]     -0.86      0.56     -0.74     -1.70     -0.08   4596.20      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    670.20      1.00\n",
+      " coefs[49]      0.03      1.00      0.04     -1.57      1.71  11583.95      1.00\n",
+      " coefs[50]     -0.87      0.57     -0.76     -1.69     -0.08   4887.46      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.14     -0.41      0.14    618.30      1.00\n",
+      " coefs[52]     -0.19      0.16     -0.19     -0.45      0.08    619.52      1.00\n",
+      " coefs[53]     -0.19      0.13     -0.18     -0.40      0.02    624.71      1.00\n",
+      " coefs[54]     -1.69      0.19     -1.68     -1.99     -1.39   4128.48      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 20 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.89      0.06      1.89      1.79      1.99   9246.42      1.00\n",
+      "  coefs[1]     -0.08      0.03     -0.08     -0.13     -0.02  11208.54      1.00\n",
+      "  coefs[2]      0.01      0.06      0.01     -0.09      0.11   3502.44      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7328.68      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   7942.68      1.00\n",
+      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11139.29      1.00\n",
+      "  coefs[6]      0.47      0.24      0.45      0.07      0.84   2645.70      1.00\n",
+      "  coefs[7]     -0.73      0.15     -0.73     -0.97     -0.49   2807.38      1.00\n",
+      "  coefs[8]      0.85      0.28      0.83      0.40      1.30   2626.09      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.01  12620.86      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.73      1.44   2934.75      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.51      0.45   2942.71      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2939.57      1.00\n",
+      " coefs[13]     -0.97      0.64     -0.91     -1.94      0.13   4606.51      1.00\n",
+      " coefs[14]     -0.46      0.66     -0.35     -1.52      0.51   5983.50      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.07   3909.10      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.62      0.11   5133.14      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.26     -0.65      0.09    826.22      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5573.30      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.56      0.56   5610.96      1.00\n",
+      " coefs[20]      0.02      0.97      0.02     -1.57      1.63  10854.73      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06    980.00      1.00\n",
+      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    642.18      1.01\n",
+      " coefs[23]      0.01      0.25      0.01     -0.39      0.44    445.60      1.01\n",
+      " coefs[24]     -0.04      0.16     -0.04     -0.30      0.23    464.65      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.32    422.35      1.01\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    425.48      1.01\n",
+      " coefs[27]     -0.70      0.61     -0.59     -1.58      0.16   5206.67      1.00\n",
+      " coefs[28]      0.03      0.99      0.04     -1.55      1.70  10690.05      1.00\n",
+      " coefs[29]      0.11      0.08      0.11     -0.02      0.23    447.83      1.01\n",
+      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    609.85      1.01\n",
+      " coefs[31]      0.03      0.08      0.03     -0.10      0.15    668.65      1.00\n",
+      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    435.76      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.39    423.61      1.01\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.77   4889.49      1.00\n",
+      " coefs[35]      0.35      0.24      0.35     -0.05      0.76    416.61      1.01\n",
+      " coefs[36]      0.32      0.31      0.32     -0.17      0.87    414.14      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.15      0.50    415.80      1.01\n",
+      " coefs[38]     -0.04      0.05     -0.04     -0.12      0.04    964.69      1.00\n",
+      " coefs[39]     -0.03      0.08     -0.02     -0.17      0.10    572.20      1.01\n",
+      " coefs[40]      0.07      0.05      0.07     -0.02      0.15    548.93      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   4809.95      1.00\n",
+      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    414.43      1.01\n",
+      " coefs[43]      0.00      0.23      0.01     -0.36      0.42    420.25      1.01\n",
+      " coefs[44]      0.18      0.22      0.19     -0.18      0.53    414.59      1.01\n",
+      " coefs[45]      0.13      0.30      0.13     -0.35      0.65    412.93      1.01\n",
+      " coefs[46]      0.22      0.28      0.22     -0.25      0.68    414.62      1.01\n",
+      " coefs[47]     -0.12      0.09     -0.12     -0.27      0.01    846.25      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.02    450.84      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.64     -0.00   5076.40      1.00\n",
+      " coefs[50]     -0.83      0.58     -0.70     -1.66     -0.04   4703.44      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.19    420.59      1.01\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    421.82      1.01\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    430.31      1.01\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   3704.67      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 21 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9762.19      1.00\n",
+      "  coefs[1]     -0.15      0.04     -0.15     -0.21     -0.09  11181.90      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3538.15      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.21   7643.43      1.00\n",
+      "  coefs[4]     -0.11      0.03     -0.11     -0.16     -0.05   8365.70      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10974.91      1.00\n",
+      "  coefs[6]      0.16      0.29      0.16     -0.31      0.64   2862.26      1.00\n",
+      "  coefs[7]     -0.60      0.18     -0.60     -0.90     -0.32   2967.20      1.00\n",
+      "  coefs[8]      0.53      0.34      0.52     -0.03      1.09   2843.52      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11309.82      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.67      1.47   3281.18      1.00\n",
+      " coefs[11]      0.01      0.29      0.01     -0.48      0.47   3284.19      1.00\n",
+      " coefs[12]      0.09      0.65      0.09     -0.96      1.18   3281.82      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.00     -0.03   4929.61      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.55   6576.05      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.66      0.04   4629.92      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5257.19      1.00\n",
+      " coefs[17]     -0.06      0.17     -0.06     -0.35      0.21    740.58      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.44   5842.99      1.00\n",
+      " coefs[19]     -0.43      0.67     -0.34     -1.50      0.63   5996.43      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.62      0.02   5050.51      1.00\n",
+      " coefs[21]     -0.77      0.60     -0.66     -1.63      0.04   4806.38      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    781.54      1.00\n",
+      " coefs[23]      0.14      0.24      0.14     -0.25      0.54    588.58      1.00\n",
+      " coefs[24]      0.05      0.15      0.05     -0.21      0.30    592.89      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.12     -0.49      0.26    569.03      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.26      0.32    570.36      1.00\n",
+      " coefs[27]     -0.70      0.62     -0.58     -1.59      0.18   5348.57      1.00\n",
+      " coefs[28]      0.03      0.99      0.02     -1.56      1.72  10094.24      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.04      0.21    603.97      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.12      0.19    749.44      1.00\n",
+      " coefs[31]     -0.00      0.08      0.00     -0.13      0.13    924.25      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.07      0.22    588.87      1.00\n",
+      " coefs[33]      0.10      0.13      0.10     -0.11      0.31    568.07      1.00\n",
+      " coefs[34]      0.14      0.06      0.14      0.04      0.24   1356.03      1.00\n",
+      " coefs[35]      0.28      0.24      0.28     -0.09      0.69    556.98      1.00\n",
+      " coefs[36]      0.31      0.31      0.31     -0.18      0.82    553.33      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    559.88      1.00\n",
+      " coefs[38]      0.01      0.03      0.01     -0.04      0.07    757.07      1.00\n",
+      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    647.92      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.04      0.12    641.85      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1297.18      1.00\n",
+      " coefs[42]      0.00      0.41      0.00     -0.64      0.69    553.97      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    559.55      1.00\n",
+      " coefs[44]      0.19      0.21      0.20     -0.15      0.54    560.54      1.00\n",
+      " coefs[45]      0.08      0.29      0.08     -0.39      0.56    556.92      1.00\n",
+      " coefs[46]      0.24      0.28      0.24     -0.18      0.72    555.62      1.00\n",
+      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    894.80      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    627.40      1.00\n",
+      " coefs[49]      0.04      1.01      0.03     -1.59      1.70  10909.59      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.09   4571.07      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.41      0.13    561.78      1.00\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.12    562.22      1.00\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.37      0.05    562.71      1.00\n",
+      " coefs[54]     -1.66      0.18     -1.65     -1.96     -1.38   4130.36      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 22 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.94      2.15   8792.94      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11601.13      1.00\n",
+      "  coefs[2]     -0.16      0.07     -0.16     -0.27     -0.05   4312.41      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   6939.66      1.00\n",
+      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.05   7411.87      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  10025.50      1.00\n",
+      "  coefs[6]     -0.04      0.25     -0.04     -0.45      0.37   3331.37      1.00\n",
+      "  coefs[7]     -0.57      0.15     -0.57     -0.82     -0.32   3563.81      1.00\n",
+      "  coefs[8]      0.29      0.29      0.29     -0.18      0.78   3339.59      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.00      0.09  10370.34      1.00\n",
+      " coefs[10]      0.39      0.66      0.39     -0.69      1.46   3233.84      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.42   3237.79      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -1.03      1.12   3237.01      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   4483.64      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.52      0.52   5759.36      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.04   4528.41      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.60      0.14   4801.30      1.00\n",
+      " coefs[17]     -0.07      0.17     -0.07     -0.35      0.22    832.85      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.42     -1.57      0.40   5510.81      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5378.76      1.00\n",
+      " coefs[20]      0.02      0.98      0.02     -1.59      1.66  12635.21      1.00\n",
+      " coefs[21]      0.00      0.03      0.00     -0.05      0.05   1578.97      1.00\n",
+      " coefs[22]      0.07      0.06      0.07     -0.03      0.15    799.11      1.00\n",
+      " coefs[23]      0.08      0.25      0.08     -0.32      0.50    631.44      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    665.12      1.00\n",
+      " coefs[25]     -0.16      0.23     -0.16     -0.52      0.25    629.61      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    649.75      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.12   4951.62      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.63      1.60   9968.12      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    691.13      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.10      0.20    752.47      1.00\n",
+      " coefs[31]      0.01      0.08      0.02     -0.12      0.14   1127.34      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    667.50      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    635.17      1.00\n",
+      " coefs[34]      0.14      0.06      0.14      0.04      0.25   1416.76      1.00\n",
+      " coefs[35]      0.33      0.25      0.33     -0.09      0.72    623.44      1.00\n",
+      " coefs[36]      0.34      0.32      0.34     -0.16      0.87    612.20      1.00\n",
+      " coefs[37]      0.15      0.20      0.15     -0.19      0.46    622.84      1.00\n",
+      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.03   1609.92      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    723.00      1.00\n",
+      " coefs[40]      0.09      0.05      0.09      0.00      0.17    829.79      1.00\n",
+      " coefs[41]      0.03      0.05      0.03     -0.05      0.12    884.95      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.64      0.73    619.81      1.00\n",
+      " coefs[43]     -0.03      0.24     -0.02     -0.43      0.34    621.58      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    617.23      1.00\n",
+      " coefs[45]      0.09      0.30      0.09     -0.39      0.60    618.28      1.00\n",
+      " coefs[46]      0.22      0.28      0.23     -0.23      0.69    608.95      1.00\n",
+      " coefs[47]     -0.02      0.06     -0.02     -0.13      0.08    790.25      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.21      0.00    689.44      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.70     -1.67      0.00   4347.16      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4436.04      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.13     -0.41      0.15    622.46      1.00\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.41      0.12    634.06      1.00\n",
+      " coefs[53]     -0.11      0.13     -0.11     -0.32      0.11    641.85      1.00\n",
+      " coefs[54]     -1.65      0.18     -1.63     -1.93     -1.33   3934.98      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 23 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.83      2.03   9689.88      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.10      0.01  12545.20      1.00\n",
+      "  coefs[2]     -0.02      0.07     -0.02     -0.13      0.09   3898.07      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   7686.11      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   8700.67      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13  10401.49      1.00\n",
+      "  coefs[6]      0.26      0.25      0.25     -0.14      0.68   2980.05      1.00\n",
+      "  coefs[7]     -0.67      0.15     -0.67     -0.92     -0.42   3112.42      1.00\n",
+      "  coefs[8]      0.57      0.29      0.56      0.11      1.07   2948.98      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  12414.78      1.00\n",
+      " coefs[10]      0.44      0.65      0.43     -0.63      1.52   2846.10      1.00\n",
+      " coefs[11]     -0.01      0.29     -0.02     -0.51      0.45   2871.59      1.00\n",
+      " coefs[12]      0.10      0.65      0.10     -0.98      1.17   2857.64      1.00\n",
+      " coefs[13]     -1.09      0.63     -1.03     -2.05     -0.01   4990.59      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.54   6165.47      1.00\n",
+      " coefs[15]     -0.81      0.57     -0.71     -1.69      0.02   5048.22      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.08   4824.68      1.00\n",
+      " coefs[17]     -0.16      0.19     -0.15     -0.48      0.13    848.87      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.40   5827.61      1.00\n",
+      " coefs[19]     -0.45      0.67     -0.36     -1.53      0.58   6544.98      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.65     -1.61      0.04   5423.70      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1947.02      1.00\n",
+      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    874.06      1.00\n",
+      " coefs[23]      0.07      0.24      0.07     -0.32      0.47    585.54      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.23    603.12      1.00\n",
+      " coefs[25]     -0.07      0.23     -0.08     -0.44      0.32    562.41      1.00\n",
+      " coefs[26]     -0.00      0.18     -0.00     -0.28      0.31    574.26      1.00\n",
+      " coefs[27]     -0.62      0.64     -0.50     -1.58      0.31   5547.06      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.58      1.68  10670.31      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.04      0.21    627.27      1.00\n",
+      " coefs[30]      0.01      0.09      0.01     -0.15      0.16    741.73      1.00\n",
+      " coefs[31]     -0.00      0.08      0.00     -0.12      0.13    840.86      1.00\n",
+      " coefs[32]      0.07      0.09      0.06     -0.08      0.21    588.23      1.00\n",
+      " coefs[33]      0.17      0.13      0.16     -0.04      0.39    570.20      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.77   5030.01      1.00\n",
+      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    559.22      1.00\n",
+      " coefs[36]      0.30      0.31      0.29     -0.20      0.82    552.54      1.00\n",
+      " coefs[37]      0.15      0.19      0.14     -0.17      0.47    551.24      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05   1035.24      1.00\n",
+      " coefs[39]     -0.00      0.08     -0.00     -0.13      0.12    664.01      1.00\n",
+      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.07    667.57      1.00\n",
+      " coefs[41]     -0.03      0.07     -0.02     -0.13      0.09   1390.68      1.00\n",
+      " coefs[42]      0.02      0.41      0.01     -0.65      0.69    555.94      1.00\n",
+      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.33    561.70      1.00\n",
+      " coefs[44]      0.16      0.21      0.15     -0.18      0.51    561.34      1.00\n",
+      " coefs[45]      0.06      0.30      0.06     -0.43      0.54    558.07      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.27      0.63    558.31      1.00\n",
+      " coefs[47]     -0.10      0.09     -0.10     -0.23      0.05   1359.88      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    608.20      1.00\n",
+      " coefs[49]      0.03      1.00      0.02     -1.51      1.75  12878.55      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.07   4962.08      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.38      0.16    577.83      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.35      0.17    562.72      1.00\n",
+      " coefs[53]     -0.11      0.13     -0.11     -0.31      0.10    564.13      1.00\n",
+      " coefs[54]     -1.61      0.18     -1.60     -1.89     -1.29   4385.25      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 24 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.07      0.06      2.07      1.97      2.18   9888.07      1.00\n",
+      "  coefs[1]     -0.04      0.04     -0.04     -0.10      0.02  10935.57      1.00\n",
+      "  coefs[2]     -0.22      0.07     -0.22     -0.34     -0.10   3416.86      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   8028.48      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8680.12      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.08  11561.50      1.00\n",
+      "  coefs[6]     -0.11      0.29     -0.11     -0.60      0.36   2742.04      1.00\n",
+      "  coefs[7]     -0.47      0.18     -0.47     -0.76     -0.17   2872.73      1.00\n",
+      "  coefs[8]      0.11      0.34      0.11     -0.46      0.65   2724.86      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  11593.39      1.00\n",
+      " coefs[10]      0.46      0.65      0.45     -0.61      1.52   3002.02      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3004.38      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -0.97      1.17   2999.89      1.00\n",
+      " coefs[13]     -1.05      0.62     -0.99     -2.05     -0.03   4368.86      1.00\n",
+      " coefs[14]     -0.46      0.68     -0.34     -1.53      0.53   5985.35      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.70      0.01   4554.68      1.00\n",
+      " coefs[16]     -0.71      0.60     -0.60     -1.63      0.13   5072.77      1.00\n",
+      " coefs[17]      0.08      0.16      0.08     -0.17      0.35    613.24      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.41   5692.96      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.37     -1.57      0.59   5682.49      1.00\n",
+      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4910.05      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1340.87      1.00\n",
+      " coefs[22]     -0.00      0.07      0.00     -0.12      0.11   1151.16      1.00\n",
+      " coefs[23]      0.19      0.25      0.19     -0.20      0.61    571.15      1.00\n",
+      " coefs[24]      0.07      0.15      0.07     -0.18      0.32    570.76      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.12     -0.52      0.25    570.00      1.00\n",
+      " coefs[26]      0.06      0.18      0.06     -0.24      0.36    570.92      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.14   4857.10      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.63      1.63  11053.83      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.10      0.15    601.17      1.00\n",
+      " coefs[30]      0.08      0.09      0.08     -0.07      0.22    653.46      1.00\n",
+      " coefs[31]      0.02      0.07      0.02     -0.10      0.14    780.03      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    587.20      1.00\n",
+      " coefs[33]      0.11      0.13      0.11     -0.10      0.33    578.82      1.00\n",
+      " coefs[34]      0.91      0.59      0.78      0.09      1.76   4633.63      1.00\n",
+      " coefs[35]      0.32      0.24      0.32     -0.10      0.70    562.55      1.00\n",
+      " coefs[36]      0.24      0.31      0.24     -0.25      0.78    550.52      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    553.24      1.00\n",
+      " coefs[38]     -0.06      0.04     -0.06     -0.12      0.00    887.46      1.00\n",
+      " coefs[39]      0.04      0.08      0.04     -0.08      0.17    641.10      1.00\n",
+      " coefs[40]      0.09      0.05      0.08      0.00      0.16    677.50      1.00\n",
+      " coefs[41]      0.03      0.05      0.03     -0.06      0.12    940.91      1.00\n",
+      " coefs[42]     -0.06      0.42     -0.06     -0.71      0.66    556.19      1.00\n",
+      " coefs[43]     -0.06      0.23     -0.06     -0.44      0.33    559.39      1.00\n",
+      " coefs[44]      0.14      0.21      0.14     -0.21      0.50    553.46      1.00\n",
+      " coefs[45]      0.07      0.30      0.07     -0.43      0.56    553.47      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.25      0.68    554.58      1.00\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    783.37      1.00\n",
+      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    604.14      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.68     -1.69     -0.01   4306.68      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   4711.24      1.00\n",
+      " coefs[51]     -0.16      0.17     -0.16     -0.43      0.13    568.23      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.15    568.33      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    579.79      1.00\n",
+      " coefs[54]     -1.60      0.18     -1.58     -1.89     -1.30   3802.32      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 25 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.91      2.12  10309.61      1.00\n",
+      "  coefs[1]     -0.03      0.03     -0.03     -0.09      0.03  12124.19      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.05   3571.48      1.00\n",
+      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.22   7482.98      1.00\n",
+      "  coefs[4]     -0.14      0.04     -0.14     -0.20     -0.08   8459.79      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10634.42      1.00\n",
+      "  coefs[6]      0.38      0.27      0.38     -0.08      0.82   2778.57      1.00\n",
+      "  coefs[7]     -0.76      0.17     -0.76     -1.02     -0.47   2903.10      1.00\n",
+      "  coefs[8]      0.74      0.32      0.74      0.20      1.26   2757.86      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  12221.01      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.69      1.46   3052.96      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.53      0.42   3052.24      1.00\n",
+      " coefs[12]      0.13      0.65      0.12     -0.94      1.21   3059.80      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.09     -0.09   4412.03      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.53      0.53   5862.03      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.65      0.05   5014.93      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.58      0.17   5030.84      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.25     -0.61      0.13   1177.44      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.43   5614.50      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.54      0.61   5929.27      1.00\n",
+      " coefs[20]      0.02      0.97      0.01     -1.48      1.69  12485.30      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1268.53      1.00\n",
+      " coefs[22]      0.06      0.05      0.06     -0.03      0.15    729.52      1.00\n",
+      " coefs[23]      0.19      0.25      0.19     -0.24      0.57    558.82      1.00\n",
+      " coefs[24]      0.05      0.16      0.05     -0.21      0.31    580.78      1.00\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.50      0.27    548.09      1.00\n",
+      " coefs[26]      0.09      0.18      0.09     -0.22      0.38    547.89      1.00\n",
+      " coefs[27]     -0.70      0.61     -0.58     -1.60      0.15   5096.35      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.66      1.61  10390.05      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    580.62      1.00\n",
+      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    628.19      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.62      0.07   4801.85      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.05      0.24    565.21      1.00\n",
+      " coefs[33]      0.15      0.13      0.16     -0.06      0.37    550.40      1.00\n",
+      " coefs[34]      0.09      0.05      0.09      0.01      0.18    895.13      1.00\n",
+      " coefs[35]      0.33      0.24      0.34     -0.07      0.74    535.96      1.00\n",
+      " coefs[36]      0.32      0.31      0.33     -0.19      0.84    533.22      1.00\n",
+      " coefs[37]      0.14      0.20      0.14     -0.20      0.45    537.09      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    939.95      1.00\n",
+      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    647.96      1.00\n",
+      " coefs[40]      0.09      0.06      0.09      0.00      0.18    799.91      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1291.14      1.00\n",
+      " coefs[42]      0.07      0.42      0.08     -0.62      0.77    533.62      1.00\n",
+      " coefs[43]     -0.02      0.23     -0.01     -0.40      0.37    534.58      1.00\n",
+      " coefs[44]      0.16      0.22      0.17     -0.20      0.51    534.54      1.00\n",
+      " coefs[45]      0.09      0.30      0.10     -0.41      0.58    533.79      1.00\n",
+      " coefs[46]      0.22      0.28      0.23     -0.26      0.66    535.06      1.00\n",
+      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    832.04      1.00\n",
+      " coefs[48]     -0.04      0.06     -0.04     -0.15      0.06    617.55      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.01   4879.90      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.73     -1.68     -0.08   4615.40      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.13     -0.43      0.13    546.89      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.16    536.48      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    552.97      1.00\n",
+      " coefs[54]     -1.76      0.19     -1.75     -2.06     -1.45   3911.71      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 26 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.95      0.06      1.95      1.85      2.05   9697.28      1.00\n",
+      "  coefs[1]     -0.01      0.03     -0.01     -0.07      0.04  12200.46      1.00\n",
+      "  coefs[2]     -0.18      0.07     -0.18     -0.28     -0.07   3835.72      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   7753.40      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8914.41      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13   9799.48      1.00\n",
+      "  coefs[6]     -0.44      0.25     -0.44     -0.83     -0.02   3083.93      1.00\n",
+      "  coefs[7]     -0.24      0.15     -0.24     -0.48      0.01   3272.49      1.00\n",
+      "  coefs[8]     -0.25      0.29     -0.24     -0.73      0.22   3069.29      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11351.99      1.00\n",
+      " coefs[10]      0.42      0.65      0.41     -0.72      1.42   3244.67      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.46   3259.76      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -1.05      1.09   3243.82      1.00\n",
+      " coefs[13]     -1.10      0.62     -1.04     -2.07     -0.06   4756.45      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.52   5832.99      1.00\n",
+      " coefs[15]     -0.81      0.57     -0.70     -1.65      0.03   4664.33      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.63      0.09   5437.49      1.00\n",
+      " coefs[17]     -0.01      0.17     -0.01     -0.27      0.27    593.91      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   5946.46      1.00\n",
+      " coefs[19]     -0.45      0.69     -0.35     -1.53      0.63   5809.86      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   4961.15      1.00\n",
+      " coefs[21]     -0.77      0.58     -0.65     -1.61      0.02   5202.46      1.00\n",
+      " coefs[22]      0.05      0.05      0.05     -0.03      0.15    658.39      1.00\n",
+      " coefs[23]      0.17      0.25      0.17     -0.23      0.58    514.11      1.00\n",
+      " coefs[24]      0.08      0.16      0.08     -0.17      0.34    523.59      1.00\n",
+      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    507.06      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    507.58      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.60     -1.61      0.13   4905.48      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.60      1.69  10750.90      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    555.98      1.00\n",
+      " coefs[30]      0.01      0.10      0.01     -0.15      0.17    672.45      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.12      0.13    807.56      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    533.46      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.07      0.38    508.16      1.00\n",
+      " coefs[34]      0.93      0.60      0.80      0.11      1.79   4631.74      1.00\n",
+      " coefs[35]      0.30      0.24      0.30     -0.08      0.73    494.20      1.00\n",
+      " coefs[36]      0.34      0.31      0.34     -0.15      0.88    494.83      1.00\n",
+      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    497.12      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.03      0.11    896.21      1.00\n",
+      " coefs[39]     -0.01      0.08     -0.00     -0.14      0.12    622.27      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.01      0.15    578.36      1.00\n",
+      " coefs[41]     -0.78      0.58     -0.66     -1.63      0.03   5017.98      1.00\n",
+      " coefs[42]      0.08      0.42      0.08     -0.62      0.76    493.89      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.43    499.52      1.00\n",
+      " coefs[44]      0.13      0.22      0.13     -0.21      0.50    496.38      1.00\n",
+      " coefs[45]      0.08      0.30      0.08     -0.44      0.56    492.93      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.28      0.65    498.64      1.00\n",
+      " coefs[47]     -0.82      0.57     -0.71     -1.67     -0.05   4656.06      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    550.33      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.67     -1.65     -0.00   4704.70      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.07   4427.45      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.17    502.20      1.00\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    502.02      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    512.18      1.00\n",
+      " coefs[54]     -1.68      0.19     -1.66     -1.96     -1.36   3876.22      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 27 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9664.80      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.11      0.00  12273.76      1.00\n",
+      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3990.60      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   8378.52      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   9122.81      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11   9835.89      1.00\n",
+      "  coefs[6]      0.43      0.28      0.43     -0.05      0.88   3212.70      1.00\n",
+      "  coefs[7]     -0.79      0.17     -0.79     -1.08     -0.52   3328.05      1.00\n",
+      "  coefs[8]      0.87      0.33      0.86      0.31      1.40   3201.38      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  12410.57      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.68      1.46   3077.07      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.56      0.40   3088.73      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.94      1.19   3080.15      1.00\n",
+      " coefs[13]     -1.00      0.63     -0.93     -2.05     -0.02   4853.41      1.00\n",
+      " coefs[14]     -0.44      0.67     -0.33     -1.47      0.59   5749.68      1.00\n",
+      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.06   4580.98      1.00\n",
+      " coefs[16]     -0.74      0.58     -0.63     -1.59      0.11   4965.06      1.00\n",
+      " coefs[17]      0.08      0.16      0.08     -0.20      0.33    757.62      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.42   5849.73      1.00\n",
+      " coefs[19]     -0.45      0.66     -0.36     -1.51      0.59   6230.51      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.61      0.03   4981.49      1.00\n",
+      " coefs[21]      0.03      0.02      0.03     -0.01      0.07   1097.70      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.05      0.14    997.56      1.00\n",
+      " coefs[23]      0.11      0.25      0.11     -0.31      0.51    703.71      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.27      0.25    725.63      1.00\n",
+      " coefs[25]     -0.05      0.23     -0.05     -0.44      0.32    685.14      1.00\n",
+      " coefs[26]      0.04      0.18      0.04     -0.26      0.33    689.06      1.00\n",
+      " coefs[27]     -0.70      0.63     -0.58     -1.63      0.17   4768.90      1.00\n",
+      " coefs[28]      0.02      1.00      0.03     -1.60      1.70  11348.00      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.11      0.15    782.70      1.00\n",
+      " coefs[30]      0.00      0.10      0.00     -0.17      0.17   1066.32      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.61      0.07   4989.76      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    711.07      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    689.21      1.00\n",
+      " coefs[34]      0.15      0.06      0.15      0.04      0.25   1520.05      1.00\n",
+      " coefs[35]      0.35      0.24      0.35     -0.05      0.75    671.45      1.00\n",
+      " coefs[36]      0.37      0.31      0.38     -0.15      0.87    674.78      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.49    677.33      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    942.01      1.00\n",
+      " coefs[39]     -0.07      0.09     -0.06     -0.21      0.07   1046.12      1.00\n",
+      " coefs[40]      0.05      0.05      0.06     -0.03      0.14    837.95      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.66     -1.65      0.04   5069.57      1.00\n",
+      " coefs[42]      0.09      0.42      0.09     -0.60      0.76    671.11      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.37      0.40    680.37      1.00\n",
+      " coefs[44]      0.17      0.21      0.18     -0.18      0.53    673.74      1.00\n",
+      " coefs[45]      0.12      0.30      0.13     -0.35      0.64    669.63      1.00\n",
+      " coefs[46]      0.25      0.28      0.25     -0.19      0.73    674.48      1.00\n",
+      " coefs[47]     -0.84      0.58     -0.71     -1.70     -0.04   4818.66      1.00\n",
+      " coefs[48]     -0.05      0.06     -0.05     -0.16      0.05    730.24      1.00\n",
+      " coefs[49]     -0.80      0.60     -0.68     -1.65      0.02   4871.11      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.08   4482.28      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    679.51      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.39      0.13    679.23      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.08    691.74      1.00\n",
+      " coefs[54]     -1.77      0.19     -1.76     -2.05     -1.45   4110.31      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 28 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.06      0.06      2.06      1.95      2.16  10589.43      1.00\n",
+      "  coefs[1]     -0.01      0.04     -0.01     -0.07      0.05  12371.89      1.00\n",
+      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3405.65      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8382.81      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   9570.33      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11  11024.17      1.00\n",
+      "  coefs[6]      0.43      0.29      0.43     -0.05      0.92   2818.87      1.00\n",
+      "  coefs[7]     -0.81      0.18     -0.80     -1.10     -0.52   2976.70      1.00\n",
+      "  coefs[8]      0.78      0.34      0.77      0.23      1.36   2826.32      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  11133.18      1.00\n",
+      " coefs[10]      0.46      0.65      0.46     -0.62      1.50   3195.00      1.00\n",
+      " coefs[11]     -0.09      0.29     -0.09     -0.56      0.39   3191.49      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -0.99      1.13   3197.02      1.00\n",
+      " coefs[13]     -0.99      0.63     -0.93     -2.01      0.02   5157.05      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.50      0.55   6122.62      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.63      0.08   4822.13      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.60      0.12   5059.19      1.00\n",
+      " coefs[17]     -0.10      0.19     -0.09     -0.41      0.20    945.77      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.56      0.41   5737.00      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5933.46      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.02   4978.14      1.00\n",
+      " coefs[21]      0.03      0.03      0.03     -0.02      0.07   1257.64      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.05      0.13    949.70      1.00\n",
+      " coefs[23]      0.08      0.24      0.09     -0.31      0.49    632.12      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.24    651.47      1.00\n",
+      " coefs[25]     -0.11      0.23     -0.10     -0.48      0.27    596.53      1.00\n",
+      " coefs[26]      0.04      0.18      0.04     -0.26      0.32    596.33      1.00\n",
+      " coefs[27]     -0.73      0.62     -0.60     -1.63      0.14   5089.50      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.63      1.64  10446.30      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.11      0.14    685.01      1.00\n",
+      " coefs[30]      0.01      0.10      0.01     -0.16      0.17    939.40      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.17      0.13   1350.65      1.00\n",
+      " coefs[32]      0.05      0.09      0.05     -0.09      0.20    622.62      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.05      0.38    604.88      1.00\n",
+      " coefs[34]      0.14      0.06      0.13      0.04      0.24   1503.83      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.06      0.72    589.40      1.00\n",
+      " coefs[36]      0.32      0.31      0.33     -0.18      0.83    582.35      1.00\n",
+      " coefs[37]      0.14      0.19      0.15     -0.17      0.46    591.16      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04    968.98      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    743.97      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.06      0.11    730.94      1.00\n",
+      " coefs[41]     -0.80      0.58     -0.68     -1.68     -0.02   5204.80      1.00\n",
+      " coefs[42]      0.01      0.41      0.02     -0.67      0.66    584.43      1.00\n",
+      " coefs[43]     -0.07      0.23     -0.07     -0.44      0.30    588.94      1.00\n",
+      " coefs[44]      0.17      0.21      0.17     -0.18      0.51    582.84      1.00\n",
+      " coefs[45]      0.17      0.29      0.18     -0.32      0.64    585.86      1.00\n",
+      " coefs[46]      0.23      0.27      0.23     -0.25      0.65    586.24      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.11     -0.26      0.02   1237.70      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.18      0.02    645.34      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1713.26      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.07   4466.26      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.11     -0.38      0.16    596.53      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    593.47      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.19     -0.41      0.00    611.55      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.41   4242.11      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 29 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09  10281.72      1.00\n",
+      "  coefs[1]     -0.08      0.03     -0.08     -0.14     -0.02  11111.60      1.00\n",
+      "  coefs[2]     -0.11      0.08     -0.11     -0.24      0.02   3283.15      1.00\n",
+      "  coefs[3]     -0.29      0.03     -0.29     -0.34     -0.23   7208.35      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8500.50      1.00\n",
+      "  coefs[5]     -0.10      0.03     -0.10     -0.16     -0.05  11522.62      1.00\n",
+      "  coefs[6]     -0.03      0.33     -0.03     -0.58      0.52   2779.03      1.00\n",
+      "  coefs[7]     -0.49      0.20     -0.49     -0.83     -0.17   2911.34      1.00\n",
+      "  coefs[8]      0.24      0.39      0.24     -0.44      0.85   2776.23      1.00\n",
+      "  coefs[9]     -0.07      0.03     -0.07     -0.11     -0.02  10734.26      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.67      1.45   3176.70      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3179.52      1.00\n",
+      " coefs[12]      0.10      0.65      0.09     -0.97      1.16   3177.55      1.00\n",
+      " coefs[13]     -1.00      0.64     -0.94     -2.00      0.02   4659.78      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.54   5589.40      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.70     -1.67      0.03   4418.25      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.61      0.12   5208.44      1.00\n",
+      " coefs[17]     -0.17      0.19     -0.16     -0.47      0.15    943.32      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.45     -1.58      0.39   5903.46      1.00\n",
+      " coefs[19]     -0.47      0.69     -0.38     -1.55      0.61   5385.20      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   5011.82      1.00\n",
+      " coefs[21]      0.04      0.03      0.04     -0.01      0.09   1530.86      1.00\n",
+      " coefs[22]      0.09      0.05      0.09      0.00      0.17    733.93      1.00\n",
+      " coefs[23]      0.04      0.25      0.04     -0.37      0.44    635.37      1.00\n",
+      " coefs[24]     -0.00      0.16     -0.01     -0.27      0.25    647.37      1.00\n",
+      " coefs[25]     -0.14      0.23     -0.14     -0.51      0.26    626.98      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.28      0.32    634.01      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.16   4950.71      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.58      1.65  10491.51      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    667.60      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.11      0.19    785.86      1.00\n",
+      " coefs[31]      0.04      0.07      0.05     -0.07      0.17    933.56      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    650.23      1.00\n",
+      " coefs[33]      0.20      0.13      0.20     -0.01      0.43    626.70      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.11      1.77   4818.61      1.00\n",
+      " coefs[35]      0.31      0.24      0.30     -0.10      0.70    609.88      1.00\n",
+      " coefs[36]      0.31      0.31      0.31     -0.21      0.82    613.54      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    621.85      1.00\n",
+      " coefs[38]     -0.02      0.05     -0.02     -0.11      0.06   1553.81      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    739.41      1.00\n",
+      " coefs[40]      0.10      0.05      0.10      0.01      0.19    890.30      1.00\n",
+      " coefs[41]     -0.01      0.07     -0.00     -0.12      0.10   1456.92      1.00\n",
+      " coefs[42]      0.02      0.42      0.01     -0.67      0.69    613.09      1.00\n",
+      " coefs[43]     -0.00      0.23     -0.01     -0.40      0.37    621.98      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.21      0.50    614.00      1.00\n",
+      " coefs[45]      0.07      0.30      0.07     -0.43      0.55    621.21      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.26      0.66    620.99      1.00\n",
+      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00   1359.24      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    644.79      1.00\n",
+      " coefs[49]     -0.82      0.60     -0.70     -1.68     -0.01   4763.74      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.72     -1.69     -0.06   4904.38      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.15    629.04      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.34      0.18    630.19      1.00\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.03    631.24      1.00\n",
+      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.34   3831.89      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 30 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.90      0.06      1.90      1.80      2.00   9019.97      1.00\n",
+      "  coefs[1]     -0.04      0.03     -0.04     -0.10      0.02  10767.61      1.00\n",
+      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3295.95      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7375.50      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   8457.63      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10886.68      1.00\n",
+      "  coefs[6]      0.50      0.29      0.50      0.03      0.97   2663.40      1.00\n",
+      "  coefs[7]     -0.78      0.18     -0.78     -1.08     -0.50   2793.04      1.00\n",
+      "  coefs[8]      0.88      0.34      0.88      0.30      1.41   2672.27      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  10751.40      1.00\n",
+      " coefs[10]      0.42      0.65      0.41     -0.61      1.51   3393.24      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3406.03      1.00\n",
+      " coefs[12]      0.07      0.65      0.07     -0.99      1.13   3403.50      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.05     -0.03   4984.38      1.00\n",
+      " coefs[14]     -0.46      0.66     -0.36     -1.47      0.53   5921.21      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.64      0.05   4545.78      1.00\n",
+      " coefs[16]     -0.73      0.57     -0.61     -1.58      0.10   5089.11      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17   1126.41      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.41   5515.73      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.57      0.56   5501.46      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   5123.43      1.00\n",
+      " coefs[21]     -0.76      0.59     -0.64     -1.61      0.05   4825.12      1.00\n",
+      " coefs[22]      0.02      0.07      0.03     -0.10      0.14   1548.35      1.00\n",
+      " coefs[23]      0.05      0.25      0.06     -0.35      0.47    783.10      1.00\n",
+      " coefs[24]      0.08      0.16      0.09     -0.16      0.35    779.21      1.00\n",
+      " coefs[25]     -0.10      0.23     -0.09     -0.49      0.28    756.44      1.00\n",
+      " coefs[26]     -0.00      0.18      0.00     -0.29      0.31    755.12      1.00\n",
+      " coefs[27]     -0.71      0.63     -0.58     -1.63      0.17   4745.70      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.54      1.73   9981.61      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    854.92      1.00\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.28      0.13   1528.49      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.64     -1.61      0.07   4759.95      1.00\n",
+      " coefs[32]      0.13      0.09      0.13     -0.02      0.27    775.07      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.05      0.39    764.75      1.00\n",
+      " coefs[34]      0.91      0.60      0.79      0.08      1.76   4523.52      1.00\n",
+      " coefs[35]      0.37      0.24      0.37     -0.02      0.79    745.02      1.01\n",
+      " coefs[36]      0.35      0.31      0.35     -0.13      0.90    743.92      1.00\n",
+      " coefs[37]      0.19      0.20      0.20     -0.13      0.52    747.52      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04   1238.03      1.00\n",
+      " coefs[39]      0.01      0.08      0.02     -0.11      0.14    874.10      1.00\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    917.48      1.00\n",
+      " coefs[41]      0.01      0.05      0.01     -0.08      0.10   1128.55      1.00\n",
+      " coefs[42]      0.05      0.41      0.05     -0.64      0.74    740.73      1.00\n",
+      " coefs[43]     -0.04      0.23     -0.04     -0.41      0.36    744.09      1.00\n",
+      " coefs[44]      0.18      0.21      0.18     -0.16      0.55    748.09      1.00\n",
+      " coefs[45]      0.15      0.30      0.16     -0.32      0.67    742.57      1.00\n",
+      " coefs[46]      0.21      0.28      0.22     -0.24      0.68    748.05      1.00\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05   1192.87      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    845.74      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.65      0.01   5087.76      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.72     -1.69     -0.05   4519.70      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.08     -0.37      0.19    749.63      1.00\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.38      0.15    752.57      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.36      0.07    766.61      1.00\n",
+      " coefs[54]     -1.70      0.19     -1.69     -2.00     -1.40   4002.84      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 31 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.89      2.10  10506.43      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11576.31      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.03   3713.76      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   8843.21      1.00\n",
+      "  coefs[4]     -0.05      0.04     -0.05     -0.10      0.01   9500.03      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10864.35      1.00\n",
+      "  coefs[6]      0.33      0.27      0.32     -0.10      0.76   2852.16      1.00\n",
+      "  coefs[7]     -0.76      0.16     -0.75     -1.01     -0.48   2964.01      1.00\n",
+      "  coefs[8]      0.69      0.31      0.68      0.19      1.20   2847.07      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11519.52      1.00\n",
+      " coefs[10]      0.39      0.65      0.39     -0.70      1.46   3245.63      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3261.90      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -0.92      1.23   3256.33      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   5056.56      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.49      0.54   6112.69      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.60      0.08   4585.07      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.61      0.11   5040.88      1.00\n",
+      " coefs[17]     -0.26      0.23     -0.25     -0.62      0.12   1111.71      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.56      0.42   5994.44      1.00\n",
+      " coefs[19]     -0.45      0.67     -0.35     -1.57      0.57   5768.92      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.01   5062.81      1.00\n",
+      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.02   5297.12      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.04      0.16    832.32      1.00\n",
+      " coefs[23]      0.14      0.25      0.14     -0.27      0.54    553.00      1.01\n",
+      " coefs[24]      0.09      0.16      0.09     -0.18      0.33    554.02      1.01\n",
+      " coefs[25]     -0.12      0.24     -0.12     -0.51      0.26    538.13      1.01\n",
+      " coefs[26]      0.03      0.18      0.03     -0.28      0.32    545.03      1.01\n",
+      " coefs[27]     -0.68      0.63     -0.56     -1.63      0.18   4961.27      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.62      1.65  10677.03      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.04      0.22    593.65      1.01\n",
+      " coefs[30]      0.07      0.09      0.07     -0.08      0.21    650.49      1.01\n",
+      " coefs[31]     -0.02      0.10     -0.02     -0.18      0.13   1189.70      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    571.81      1.01\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.38    540.11      1.01\n",
+      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1289.56      1.00\n",
+      " coefs[35]      0.35      0.25      0.35     -0.06      0.74    528.74      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.22      0.81    527.93      1.01\n",
+      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    535.58      1.01\n",
+      " coefs[38]     -0.82      0.58     -0.69     -1.66     -0.03   5038.93      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    632.38      1.01\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    644.97      1.01\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.66      0.03   4898.98      1.00\n",
+      " coefs[42]      0.04      0.42      0.05     -0.68      0.69    530.13      1.01\n",
+      " coefs[43]      0.00      0.23      0.01     -0.38      0.38    535.88      1.01\n",
+      " coefs[44]      0.18      0.22      0.18     -0.19      0.52    531.17      1.01\n",
+      " coefs[45]      0.11      0.30      0.11     -0.39      0.60    527.06      1.01\n",
+      " coefs[46]      0.26      0.28      0.26     -0.21      0.71    527.83      1.01\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    742.72      1.01\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    592.25      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.65      0.01   4900.71      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.75     -1.71     -0.09   4640.27      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.16    539.58      1.01\n",
+      " coefs[52]     -0.10      0.16     -0.10     -0.38      0.15    540.36      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    553.93      1.01\n",
+      " coefs[54]     -1.79      0.19     -1.77     -2.09     -1.49   4183.29      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 32 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.93      2.14  10125.47      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.09      0.03  11574.62      1.00\n",
+      "  coefs[2]     -0.05      0.08     -0.05     -0.17      0.08   3281.43      1.00\n",
+      "  coefs[3]     -0.35      0.03     -0.35     -0.41     -0.29   7593.31      1.00\n",
+      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8084.89      1.00\n",
+      "  coefs[5]     -0.13      0.03     -0.13     -0.19     -0.08  10905.67      1.00\n",
+      "  coefs[6]     -0.31      0.31     -0.30     -0.82      0.18   2706.12      1.00\n",
+      "  coefs[7]     -0.31      0.19     -0.31     -0.64     -0.02   2873.98      1.00\n",
+      "  coefs[8]     -0.05      0.36     -0.04     -0.64      0.54   2711.99      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.01  11662.00      1.00\n",
+      " coefs[10]      0.36      0.65      0.35     -0.70      1.45   3104.82      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3113.43      1.00\n",
+      " coefs[12]      0.13      0.65      0.11     -0.91      1.23   3110.90      1.00\n",
+      " coefs[13]     -0.92      0.65     -0.85     -1.98      0.10   4557.60      1.00\n",
+      " coefs[14]     -0.48      0.67     -0.37     -1.53      0.52   5472.45      1.00\n",
+      " coefs[15]     -0.77      0.57     -0.67     -1.66      0.05   4497.69      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.10   5133.58      1.00\n",
+      " coefs[17]     -0.19      0.19     -0.18     -0.49      0.11    650.98      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.45     -1.58      0.38   5533.20      1.00\n",
+      " coefs[19]     -0.48      0.68     -0.39     -1.60      0.56   5797.66      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5225.53      1.00\n",
+      " coefs[21]      0.85      0.59      0.73      0.05      1.69   4743.33      1.00\n",
+      " coefs[22]      0.08      0.06      0.08     -0.01      0.17    616.41      1.00\n",
+      " coefs[23]     -0.12      0.26     -0.12     -0.55      0.27    509.35      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.26      0.26    505.07      1.00\n",
+      " coefs[25]     -0.06      0.23     -0.06     -0.46      0.31    470.64      1.00\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.32      0.28    466.27      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.11   4885.26      1.00\n",
+      " coefs[28]      0.02      1.00      0.03     -1.53      1.77  10588.75      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.07      0.18    499.21      1.00\n",
+      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    651.77      1.00\n",
+      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13    974.28      1.00\n",
+      " coefs[32]      0.13      0.09      0.13     -0.02      0.28    487.05      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    456.31      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4689.58      1.00\n",
+      " coefs[35]      0.36      0.24      0.36     -0.03      0.77    458.75      1.00\n",
+      " coefs[36]      0.36      0.31      0.36     -0.15      0.86    453.29      1.00\n",
+      " coefs[37]      0.13      0.20      0.13     -0.18      0.46    457.34      1.00\n",
+      " coefs[38]      0.00      0.05      0.01     -0.08      0.09   1270.06      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    528.49      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    533.76      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1041.39      1.00\n",
+      " coefs[42]      0.09      0.42      0.08     -0.61      0.74    455.70      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.35      0.40    460.85      1.00\n",
+      " coefs[44]      0.14      0.22      0.15     -0.22      0.49    447.48      1.00\n",
+      " coefs[45]      0.10      0.30      0.10     -0.39      0.58    452.15      1.00\n",
+      " coefs[46]      0.17      0.28      0.17     -0.28      0.63    450.76      1.00\n",
+      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00    959.11      1.00\n",
+      " coefs[48]     -0.04      0.06     -0.04     -0.14      0.07    493.15      1.00\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.01   4845.43      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4590.09      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.15     -0.43      0.12    466.09      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.37      0.15    465.86      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    473.04      1.00\n",
+      " coefs[54]     -1.67      0.19     -1.66     -1.97     -1.36   4072.51      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 33 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.91      0.06      1.91      1.81      2.01  10511.47      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12220.55      1.00\n",
+      "  coefs[2]     -0.07      0.07     -0.07     -0.19      0.04   3687.76      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   7665.75      1.00\n",
+      "  coefs[4]     -0.06      0.03     -0.06     -0.11     -0.00   9077.63      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  11684.74      1.00\n",
+      "  coefs[6]      0.26      0.29      0.25     -0.20      0.75   2923.46      1.00\n",
+      "  coefs[7]     -0.61      0.18     -0.61     -0.89     -0.31   3050.64      1.00\n",
+      "  coefs[8]      0.61      0.34      0.60      0.07      1.20   2919.52      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11351.45      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.73      1.41   3228.80      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.41   3241.45      1.00\n",
+      " coefs[12]      0.11      0.64      0.11     -1.00      1.13   3238.02      1.00\n",
+      " coefs[13]     -0.97      0.64     -0.91     -1.98      0.07   5249.99      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.48      0.54   6066.89      1.00\n",
+      " coefs[15]     -0.77      0.56     -0.67     -1.64      0.04   4986.07      1.00\n",
+      " coefs[16]     -0.73      0.58     -0.62     -1.61      0.09   5444.07      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17    776.12      1.00\n",
+      " coefs[18]     -0.53      0.67     -0.42     -1.55      0.44   6209.21      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.39     -1.57      0.55   6230.36      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   5067.27      1.00\n",
+      " coefs[21]     -0.76      0.58     -0.65     -1.59      0.05   5458.41      1.00\n",
+      " coefs[22]     -0.00      0.07      0.00     -0.12      0.12   1121.18      1.00\n",
+      " coefs[23]      0.03      0.25      0.04     -0.37      0.44    541.73      1.00\n",
+      " coefs[24]      0.02      0.16      0.02     -0.24      0.27    539.71      1.00\n",
+      " coefs[25]     -0.05      0.23     -0.06     -0.43      0.33    515.63      1.00\n",
+      " coefs[26]      0.05      0.18      0.05     -0.24      0.35    517.55      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.60      0.15   5250.27      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.58      1.68  11408.51      1.00\n",
+      " coefs[29]      0.10      0.08      0.10     -0.03      0.22    537.16      1.00\n",
+      " coefs[30]      0.03      0.09      0.04     -0.11      0.18    614.05      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1169.25      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    546.97      1.00\n",
+      " coefs[33]      0.17      0.13      0.17     -0.04      0.39    519.49      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.11      1.76   4777.97      1.00\n",
+      " coefs[35]      0.37      0.25      0.37     -0.01      0.78    501.98      1.00\n",
+      " coefs[36]      0.36      0.31      0.36     -0.17      0.85    498.97      1.00\n",
+      " coefs[37]      0.20      0.20      0.20     -0.13      0.51    509.05      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.04    846.24      1.00\n",
+      " coefs[39]     -0.02      0.08     -0.02     -0.14      0.12    639.66      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.06      0.10    608.38      1.00\n",
+      " coefs[41]     -0.80      0.59     -0.68     -1.66      0.01   4980.95      1.00\n",
+      " coefs[42]      0.09      0.42      0.09     -0.57      0.79    505.92      1.00\n",
+      " coefs[43]      0.01      0.23      0.00     -0.37      0.39    510.07      1.00\n",
+      " coefs[44]      0.17      0.22      0.17     -0.17      0.53    501.53      1.00\n",
+      " coefs[45]      0.08      0.30      0.08     -0.42      0.56    499.88      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.29      0.62    505.21      1.00\n",
+      " coefs[47]     -0.86      0.57     -0.74     -1.70     -0.06   4649.67      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    529.40      1.00\n",
+      " coefs[49]      0.04      1.00      0.02     -1.59      1.66  12157.87      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.73     -1.71     -0.08   4732.51      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.16    504.47      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.33      0.19    511.03      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.07    515.84      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4097.08      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 34 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.05      0.06      2.05      1.95      2.16  10000.30      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.01     -0.07      0.05  10626.97      1.00\n",
+      "  coefs[2]     -0.14      0.07     -0.14     -0.26     -0.02   3772.39      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.41     -0.30   7420.44      1.00\n",
+      "  coefs[4]     -0.05      0.03     -0.05     -0.11      0.01   8047.09      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  10672.51      1.00\n",
+      "  coefs[6]     -0.17      0.28     -0.17     -0.63      0.30   3074.31      1.00\n",
+      "  coefs[7]     -0.40      0.17     -0.40     -0.69     -0.13   3264.91      1.00\n",
+      "  coefs[8]      0.07      0.33      0.07     -0.46      0.63   3067.33      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11678.49      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.61      1.54   3198.32      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.57      0.39   3220.36      1.00\n",
+      " coefs[12]      0.08      0.65      0.08     -1.01      1.14   3215.87      1.00\n",
+      " coefs[13]     -1.07      0.62     -1.01     -2.06     -0.07   4551.88      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.54   6254.49      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.63      0.06   4416.51      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.60     -1.60      0.13   4831.45      1.00\n",
+      " coefs[17]      0.01      0.17      0.01     -0.26      0.28    591.23      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   6005.73      1.00\n",
+      " coefs[19]     -0.45      0.69     -0.36     -1.53      0.63   5509.96      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5084.54      1.00\n",
+      " coefs[21]      0.05      0.03      0.04     -0.01      0.10   1382.99      1.00\n",
+      " coefs[22]      0.10      0.05      0.10      0.02      0.19    596.70      1.00\n",
+      " coefs[23]      0.12      0.25      0.12     -0.30      0.51    508.75      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.23      0.28    514.96      1.00\n",
+      " coefs[25]     -0.10      0.24     -0.11     -0.49      0.27    492.31      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    498.67      1.00\n",
+      " coefs[27]     -0.71      0.61     -0.60     -1.61      0.13   4956.76      1.00\n",
+      " coefs[28]      0.01      0.99      0.01     -1.54      1.69  11010.12      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    556.65      1.00\n",
+      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    614.00      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.12      0.14    795.57      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    512.23      1.00\n",
+      " coefs[33]      0.13      0.13      0.13     -0.09      0.35    502.30      1.00\n",
+      " coefs[34]      0.91      0.59      0.80      0.12      1.77   4902.15      1.00\n",
+      " coefs[35]      0.30      0.25      0.29     -0.11      0.70    491.25      1.00\n",
+      " coefs[36]      0.32      0.32      0.32     -0.20      0.82    483.51      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.17      0.47    490.31      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.03    803.24      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    590.41      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    588.34      1.00\n",
+      " coefs[41]      0.01      0.07      0.01     -0.10      0.12   1292.79      1.00\n",
+      " coefs[42]     -0.02      0.42     -0.02     -0.71      0.65    487.70      1.00\n",
+      " coefs[43]     -0.03      0.23     -0.04     -0.42      0.34    497.84      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    490.22      1.00\n",
+      " coefs[45]      0.10      0.30      0.10     -0.39      0.60    486.10      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.27      0.64    490.41      1.00\n",
+      " coefs[47]     -0.86      0.56     -0.75     -1.70     -0.08   4880.99      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.05    543.91      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.70     -1.66      0.01   4856.94      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.72     -1.70     -0.06   4479.77      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.12    499.77      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.13     -0.38      0.14    497.92      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    497.46      1.00\n",
+      " coefs[54]     -1.64      0.18     -1.62     -1.92     -1.33   3835.59      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 35 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.07   9742.14      1.00\n",
+      "  coefs[1]     -0.06      0.04     -0.06     -0.12     -0.00  10941.17      1.00\n",
+      "  coefs[2]     -0.15      0.07     -0.15     -0.27     -0.04   3797.76      1.00\n",
+      "  coefs[3]     -0.37      0.03     -0.37     -0.42     -0.31   7795.70      1.00\n",
+      "  coefs[4]     -0.03      0.03     -0.03     -0.09      0.03   8579.09      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.24     -0.13  10418.88      1.00\n",
+      "  coefs[6]      0.05      0.28      0.05     -0.39      0.52   2999.81      1.00\n",
+      "  coefs[7]     -0.57      0.17     -0.57     -0.85     -0.29   3099.11      1.00\n",
+      "  coefs[8]      0.46      0.33      0.46     -0.08      0.99   3002.13      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  10895.90      1.00\n",
+      " coefs[10]      0.47      0.64      0.48     -0.58      1.53   3303.11      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.49      0.44   3312.49      1.00\n",
+      " coefs[12]      0.07      0.64      0.07     -1.00      1.10   3315.68      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.00     -2.06     -0.09   4977.49      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.45      0.58   5820.49      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.65      0.06   4544.59      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.59      0.10   4799.76      1.00\n",
+      " coefs[17]      0.03      0.16      0.04     -0.24      0.30    739.13      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.58      0.40   6011.13      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.56   5503.24      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.63      0.02   4644.05      1.00\n",
+      " coefs[21]     -0.78      0.58     -0.66     -1.63      0.01   4745.88      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    873.25      1.01\n",
+      " coefs[23]      0.09      0.25      0.09     -0.31      0.51    688.44      1.01\n",
+      " coefs[24]      0.03      0.16      0.03     -0.22      0.30    737.69      1.01\n",
+      " coefs[25]     -0.05      0.23     -0.04     -0.42      0.36    662.47      1.01\n",
+      " coefs[26]      0.05      0.18      0.06     -0.24      0.36    675.97      1.01\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.61      0.11   4795.73      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.61      1.69  10020.48      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    720.56      1.01\n",
+      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    833.72      1.01\n",
+      " coefs[31]      0.02      0.08      0.02     -0.11      0.15   1020.81      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    684.55      1.01\n",
+      " coefs[33]      0.14      0.13      0.14     -0.07      0.36    677.90      1.01\n",
+      " coefs[34]      0.13      0.06      0.12      0.03      0.23   1738.80      1.00\n",
+      " coefs[35]      0.28      0.24      0.29     -0.13      0.67    646.54      1.01\n",
+      " coefs[36]      0.28      0.31      0.29     -0.23      0.81    657.65      1.01\n",
+      " coefs[37]      0.21      0.20      0.21     -0.11      0.54    652.29      1.01\n",
+      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    862.31      1.01\n",
+      " coefs[39]     -0.02      0.08     -0.02     -0.15      0.12    869.75      1.01\n",
+      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    755.29      1.01\n",
+      " coefs[41]      0.03      0.05      0.03     -0.06      0.12   1142.51      1.00\n",
+      " coefs[42]     -0.00      0.42      0.00     -0.67      0.72    652.36      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.41      0.36    663.81      1.01\n",
+      " coefs[44]      0.14      0.22      0.14     -0.22      0.50    651.86      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.44      0.56    654.79      1.01\n",
+      " coefs[46]      0.19      0.28      0.20     -0.25      0.68    656.43      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05    993.49      1.00\n",
+      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    734.51      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.64      0.03   4950.47      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.08   4526.96      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.15    668.74      1.01\n",
+      " coefs[52]     -0.12      0.16     -0.11     -0.38      0.15    669.40      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    676.97      1.01\n",
+      " coefs[54]     -1.65      0.18     -1.64     -1.93     -1.34   4116.09      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 36 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.96      0.06      1.96      1.86      2.06   9372.47      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  10822.01      1.00\n",
+      "  coefs[2]     -0.17      0.06     -0.17     -0.27     -0.07   3864.52      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   7410.99      1.00\n",
+      "  coefs[4]     -0.05      0.03     -0.05     -0.10      0.01   8105.01      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.06  10915.47      1.00\n",
+      "  coefs[6]     -0.03      0.22     -0.03     -0.40      0.33   2760.58      1.00\n",
+      "  coefs[7]     -0.48      0.13     -0.48     -0.69     -0.26   3090.19      1.00\n",
+      "  coefs[8]      0.28      0.25      0.27     -0.12      0.72   2820.91      1.00\n",
+      "  coefs[9]     -0.02      0.03     -0.02     -0.07      0.03  11238.51      1.00\n",
+      " coefs[10]      0.40      0.65      0.40     -0.71      1.44   3232.80      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3242.27      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.97      1.18   3245.95      1.00\n",
+      " coefs[13]     -1.05      0.63     -1.00     -2.09     -0.07   5192.61      1.00\n",
+      " coefs[14]     -0.44      0.68     -0.33     -1.49      0.58   5836.55      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.69     -1.65      0.04   4569.53      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.65      0.09   5300.47      1.00\n",
+      " coefs[17]     -0.02      0.17     -0.02     -0.29      0.28    807.36      1.01\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5962.50      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.57      0.57   5232.08      1.00\n",
+      " coefs[20]      0.02      0.98      0.03     -1.59      1.63  12107.78      1.00\n",
+      " coefs[21]     -0.77      0.60     -0.64     -1.63      0.05   4698.56      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.00      0.17    756.90      1.01\n",
+      " coefs[23]      0.11      0.26      0.11     -0.32      0.52    701.29      1.01\n",
+      " coefs[24]      0.06      0.16      0.06     -0.21      0.31    635.73      1.01\n",
+      " coefs[25]     -0.06      0.24     -0.06     -0.48      0.31    644.03      1.01\n",
+      " coefs[26]     -0.01      0.19     -0.01     -0.31      0.30    665.28      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.59      0.12   5029.47      1.00\n",
+      " coefs[28]      0.03      1.00      0.02     -1.63      1.65  10008.37      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.12      0.15    712.05      1.01\n",
+      " coefs[30]      0.03      0.09      0.03     -0.12      0.18    801.77      1.01\n",
+      " coefs[31]     -0.05      0.10     -0.05     -0.20      0.11   1444.46      1.01\n",
+      " coefs[32]      0.13      0.09      0.13     -0.03      0.27    721.44      1.01\n",
+      " coefs[33]      0.11      0.14      0.12     -0.12      0.32    656.94      1.01\n",
+      " coefs[34]      0.91      0.60      0.78      0.09      1.79   4477.44      1.00\n",
+      " coefs[35]      0.29      0.25      0.29     -0.14      0.68    652.55      1.01\n",
+      " coefs[36]      0.30      0.32      0.30     -0.27      0.78    645.31      1.01\n",
+      " coefs[37]      0.12      0.20      0.13     -0.22      0.44    649.06      1.01\n",
+      " coefs[38]      0.00      0.03      0.00     -0.06      0.06    814.07      1.01\n",
+      " coefs[39]     -0.01      0.08     -0.01     -0.15      0.13    885.40      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    786.68      1.01\n",
+      " coefs[41]      0.01      0.06      0.01     -0.08      0.10   1079.71      1.01\n",
+      " coefs[42]      0.03      0.43      0.03     -0.71      0.69    657.11      1.01\n",
+      " coefs[43]     -0.04      0.24     -0.04     -0.45      0.34    660.02      1.01\n",
+      " coefs[44]      0.12      0.22      0.12     -0.26      0.46    643.07      1.01\n",
+      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    656.44      1.01\n",
+      " coefs[46]      0.22      0.29      0.22     -0.26      0.68    652.23      1.01\n",
+      " coefs[47]     -0.05      0.07     -0.05     -0.17      0.07   1065.65      1.01\n",
+      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    689.46      1.01\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4683.36      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4867.74      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.16    682.73      1.01\n",
+      " coefs[52]     -0.14      0.17     -0.14     -0.43      0.11    670.78      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.05    678.49      1.01\n",
+      " coefs[54]     -1.63      0.18     -1.61     -1.92     -1.32   3991.08      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 37 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.12  10190.29      1.00\n",
+      "  coefs[1]      0.03      0.04      0.03     -0.03      0.09  11618.83      1.00\n",
+      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.04   3901.96      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   8168.46      1.00\n",
+      "  coefs[4]     -0.06      0.04     -0.06     -0.12     -0.00   9352.54      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.17     -0.23     -0.12  11575.01      1.00\n",
+      "  coefs[6]      0.44      0.27      0.42     -0.00      0.87   3054.71      1.00\n",
+      "  coefs[7]     -0.85      0.16     -0.84     -1.11     -0.58   3227.23      1.00\n",
+      "  coefs[8]      0.81      0.31      0.80      0.29      1.31   3054.83      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11497.32      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.66      1.50   3059.84      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.57      0.39   3069.11      1.00\n",
+      " coefs[12]      0.05      0.65      0.04     -1.03      1.12   3065.23      1.00\n",
+      " coefs[13]     -0.95      0.64     -0.89     -1.95      0.10   5155.64      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.46      0.60   6013.74      1.00\n",
+      " coefs[15]     -0.76      0.58     -0.65     -1.62      0.10   4813.79      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.57      0.16   5147.70      1.00\n",
+      " coefs[17]     -0.85      0.55     -0.76     -1.68     -0.01   4545.60      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.43     -1.54      0.44   6040.82      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.37     -1.57      0.55   6180.31      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.04   5180.47      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5257.24      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.13    996.95      1.00\n",
+      " coefs[23]      0.05      0.24      0.05     -0.38      0.42    686.43      1.00\n",
+      " coefs[24]      0.14      0.15      0.14     -0.12      0.38    671.57      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.11     -0.49      0.26    670.77      1.00\n",
+      " coefs[26]      0.11      0.18      0.12     -0.18      0.39    661.76      1.00\n",
+      " coefs[27]     -0.70      0.62     -0.59     -1.60      0.17   5031.16      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.63      1.68  10507.75      1.00\n",
+      " coefs[29]      0.03      0.08      0.03     -0.10      0.16    760.67      1.00\n",
+      " coefs[30]      0.10      0.09      0.10     -0.05      0.24    811.00      1.00\n",
+      " coefs[31]     -0.76      0.59     -0.63     -1.60      0.08   4563.06      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    686.24      1.00\n",
+      " coefs[33]      0.18      0.13      0.18     -0.03      0.39    665.40      1.00\n",
+      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4500.21      1.00\n",
+      " coefs[35]      0.39      0.24      0.40     -0.02      0.76    645.92      1.00\n",
+      " coefs[36]      0.43      0.31      0.43     -0.11      0.90    646.61      1.00\n",
+      " coefs[37]      0.20      0.19      0.20     -0.13      0.50    649.74      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    945.88      1.00\n",
+      " coefs[39]      0.04      0.08      0.04     -0.09      0.16    786.82      1.00\n",
+      " coefs[40]      0.12      0.05      0.12      0.03      0.20    849.33      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   5036.10      1.00\n",
+      " coefs[42]      0.02      0.41      0.03     -0.70      0.64    646.14      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.39      0.36    650.33      1.00\n",
+      " coefs[44]      0.23      0.21      0.23     -0.16      0.53    641.32      1.00\n",
+      " coefs[45]      0.16      0.29      0.17     -0.35      0.62    645.40      1.00\n",
+      " coefs[46]      0.28      0.27      0.28     -0.20      0.70    644.22      1.00\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.16      0.07    992.72      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.03    734.82      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.04   1801.99      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.74     -1.69     -0.05   4857.12      1.00\n",
+      " coefs[51]     -0.08      0.17     -0.08     -0.38      0.17    656.17      1.00\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.34      0.17    660.34      1.00\n",
+      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.05    673.66      1.00\n",
+      " coefs[54]     -1.86      0.20     -1.84     -2.17     -1.51   4098.42      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 38 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.96      1.87      2.07  10096.48      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12244.36      1.00\n",
+      "  coefs[2]     -0.04      0.06     -0.04     -0.15      0.07   4159.98      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.38     -0.27   7749.88      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8882.58      1.00\n",
+      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11482.48      1.00\n",
+      "  coefs[6]      0.07      0.24      0.06     -0.32      0.47   3120.93      1.00\n",
+      "  coefs[7]     -0.51      0.15     -0.51     -0.75     -0.26   3283.63      1.00\n",
+      "  coefs[8]      0.42      0.28      0.42     -0.05      0.87   3098.35      1.00\n",
+      "  coefs[9]     -0.06      0.03     -0.06     -0.11     -0.01  11951.39      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.62      1.53   3260.72      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.05     -0.56      0.40   3274.76      1.00\n",
+      " coefs[12]      0.06      0.65      0.05     -1.00      1.15   3282.00      1.00\n",
+      " coefs[13]     -1.05      0.62     -1.00     -2.12     -0.12   5389.23      1.00\n",
+      " coefs[14]     -0.46      0.68     -0.35     -1.52      0.56   6658.42      1.00\n",
+      " coefs[15]     -0.79      0.56     -0.69     -1.65      0.05   5438.21      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5338.59      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.25     -0.63      0.11   1265.14      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.46     -1.59      0.38   5781.56      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.36     -1.53      0.61   6188.61      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.04   5486.01      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1964.40      1.00\n",
+      " coefs[22]      0.01      0.07      0.01     -0.11      0.13   1235.89      1.00\n",
+      " coefs[23]      0.10      0.25      0.10     -0.32      0.49    591.69      1.00\n",
+      " coefs[24]      0.08      0.16      0.08     -0.19      0.32    595.98      1.00\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.47      0.30    576.69      1.00\n",
+      " coefs[26]      0.03      0.18      0.03     -0.26      0.33    584.84      1.00\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.14   5240.14      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.68  11781.73      1.00\n",
+      " coefs[29]      0.06      0.08      0.07     -0.06      0.19    634.64      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.12      0.18    665.09      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.64     -1.62      0.05   4939.89      1.00\n",
+      " coefs[32]      0.04      0.09      0.04     -0.10      0.19    595.34      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.38    588.17      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.77   4449.06      1.00\n",
+      " coefs[35]      0.29      0.24      0.30     -0.12      0.68    566.20      1.00\n",
+      " coefs[36]      0.35      0.31      0.35     -0.19      0.84    565.96      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.12      0.52    569.22      1.00\n",
+      " coefs[38]     -0.06      0.04     -0.05     -0.12      0.01    935.97      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    737.66      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    682.67      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1363.24      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.64      0.72    564.74      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.38      0.39    570.94      1.00\n",
+      " coefs[44]      0.18      0.21      0.19     -0.18      0.53    568.55      1.00\n",
+      " coefs[45]      0.15      0.30      0.15     -0.35      0.63    562.05      1.00\n",
+      " coefs[46]      0.23      0.28      0.23     -0.24      0.68    565.69      1.00\n",
+      " coefs[47]     -0.84      0.57     -0.72     -1.69     -0.04   4863.24      1.00\n",
+      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    649.56      1.00\n",
+      " coefs[49]      0.03      1.01      0.02     -1.55      1.72  11743.21      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   5084.52      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.09     -0.38      0.18    574.15      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.41      0.12    576.37      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.17     -0.39      0.03    578.29      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.69     -2.00     -1.38   4122.53      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 39 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.13  10022.35      1.00\n",
+      "  coefs[1]     -0.07      0.04     -0.07     -0.13     -0.02  11930.67      1.00\n",
+      "  coefs[2]      0.09      0.07      0.09     -0.03      0.21   3565.47      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   7874.95      1.00\n",
+      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.04   8677.59      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11143.46      1.00\n",
+      "  coefs[6]      0.64      0.30      0.63      0.17      1.14   2850.68      1.00\n",
+      "  coefs[7]     -0.90      0.18     -0.89     -1.21     -0.61   3006.07      1.00\n",
+      "  coefs[8]      1.05      0.35      1.04      0.50      1.63   2848.02      1.00\n",
+      "  coefs[9]      0.05      0.03      0.05      0.00      0.10  11434.28      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.73      1.41   3027.13      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.05     -0.56      0.40   3049.82      1.00\n",
+      " coefs[12]      0.14      0.65      0.14     -0.93      1.20   3039.84      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.94     -2.00     -0.00   4993.50      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.53   5614.94      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.06   4675.04      1.00\n",
+      " coefs[16]     -0.70      0.58     -0.59     -1.57      0.15   5153.50      1.00\n",
+      " coefs[17]     -0.05      0.17     -0.04     -0.32      0.23    652.24      1.01\n",
+      " coefs[18]     -0.52      0.66     -0.40     -1.52      0.44   6037.65      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.36     -1.55      0.61   6114.54      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.02   4987.38      1.00\n",
+      " coefs[21]     -0.75      0.59     -0.64     -1.59      0.05   4951.24      1.00\n",
+      " coefs[22]     -0.75      0.60     -0.63     -1.63      0.05   4435.53      1.00\n",
+      " coefs[23]      0.12      0.24      0.12     -0.27      0.51    500.82      1.01\n",
+      " coefs[24]      0.03      0.15      0.03     -0.24      0.26    526.83      1.01\n",
+      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.33    494.40      1.01\n",
+      " coefs[26]      0.01      0.17      0.01     -0.28      0.30    506.35      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.59      0.16   5403.79      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.55      1.70  10861.75      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    543.44      1.01\n",
+      " coefs[30]      0.08      0.09      0.08     -0.06      0.22    601.06      1.01\n",
+      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13   1105.50      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    526.65      1.01\n",
+      " coefs[33]      0.12      0.13      0.12     -0.10      0.32    494.20      1.01\n",
+      " coefs[34]      0.93      0.59      0.81      0.12      1.79   4585.26      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    491.75      1.01\n",
+      " coefs[36]      0.37      0.30      0.37     -0.14      0.86    486.39      1.01\n",
+      " coefs[37]      0.15      0.19      0.15     -0.16      0.47    488.15      1.01\n",
+      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    676.92      1.01\n",
+      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    570.31      1.01\n",
+      " coefs[40]      0.02      0.05      0.03     -0.05      0.11    563.75      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.66     -1.63      0.03   4822.95      1.00\n",
+      " coefs[42]      0.05      0.40      0.06     -0.59      0.74    487.94      1.01\n",
+      " coefs[43]      0.01      0.23      0.01     -0.36      0.38    491.71      1.01\n",
+      " coefs[44]      0.19      0.21      0.20     -0.17      0.52    491.92      1.01\n",
+      " coefs[45]      0.07      0.29      0.08     -0.42      0.53    489.32      1.01\n",
+      " coefs[46]      0.20      0.27      0.20     -0.26      0.63    486.73      1.01\n",
+      " coefs[47]     -0.10      0.07     -0.10     -0.21      0.01    773.52      1.01\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.02    540.35      1.01\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.66     -0.02   4748.32      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.70     -0.08   4705.07      1.00\n",
+      " coefs[51]     -0.13      0.16     -0.13     -0.40      0.14    498.31      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    504.10      1.01\n",
+      " coefs[53]     -0.15      0.13     -0.14     -0.35      0.06    502.86      1.01\n",
+      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   4340.91      1.00\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(1), K)\n",
+    "subposteriors = []\n",
+    "for i, (rng, shard) in enumerate(zip(rngs, shards)):\n",
+    "    sep = '=' * 31\n",
+    "    print('\\n ' + sep + ' SUBPOSTERIOR {:02d} '.format(i) + sep, end='')\n",
+    "    samples = get_subposterior(rng, shard, K)\n",
+    "    if not os.path.exists('.results'):\n",
+    "        os.makedir('.results')\n",
+    "    np.save('.results/subposterior_{:02d}.npy'.format(i), samples)\n",
+    "    subposteriors.append(samples)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### merge subposteriors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "consensus_samples = consensus(subposteriors, 10000)\n",
+    "parametric_samples = parametric_draws(subposteriors, 10000)\n",
+    "np.save('.results/consensus_samples.npy', consensus_samples)\n",
+    "np.save('.results/parametric_samples.npy', parametric_samples)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### predict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def predict(model, X, rng, sample):\n",
+    "    model = substitute(seed(model, rng), sample)\n",
+    "    model_trace = trace(model).get_trace(X, None)\n",
+    "    return model_trace['y']['value']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Consensus accuaracy: 0.771\n",
+      "Parametric accuaracy: 0.771\n"
+     ]
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(2), 10000)\n",
+    "\n",
+    "y_consensus = vmap(partial(predict, model, X_test))(rngs, consensus_samples)\n",
+    "y_consensus = (y_consensus.sum(axis=0) / y_consensus.shape[0]) >= 0.5\n",
+    "acc = (y_consensus == y_test).sum() / y_test.shape[0]\n",
+    "print('Consensus accuaracy: {}'.format(round(acc.item(), 4)))\n",
+    "\n",
+    "y_parametric = vmap(partial(predict, model, X_test))(rngs, parametric_samples)\n",
+    "y_parametric = (y_parametric.sum(axis=0) / y_parametric.shape[0]) >= 0.5\n",
+    "acc = (y_parametric == y_test).sum() / y_test.shape[0]\n",
+    "print('Parametric accuaracy: {}'.format(round(acc.item(), 4)))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python (test)",
+   "language": "python",
+   "name": "test"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From 0fcfb1dcbe007e0f55c11746fe0498263b2921dc Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Fri, 9 Aug 2019 08:49:07 -0400
Subject: [PATCH 20/35] temporary save

---
 notebooks/source/covtype.ipynb | 89 +++++++++++++++++++++++++++++++---
 1 file changed, 81 insertions(+), 8 deletions(-)

diff --git a/notebooks/source/covtype.ipynb b/notebooks/source/covtype.ipynb
index e3975a88b..8d3982e5c 100644
--- a/notebooks/source/covtype.ipynb
+++ b/notebooks/source/covtype.ipynb
@@ -2,24 +2,28 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [],
    "source": [
     "from functools import partial\n",
     "import os; os.environ['XLA_FLAGS'] = '--xla_force_host_platform_device_count=4'\n",
     "\n",
+    "import matplotlib.pyplot as plt\n",
     "import numpy as onp\n",
     "\n",
-    "from jax import jit, random, vmap\n",
+    "from jax import jit, lax, random, vmap\n",
     "from jax.config import config; config.update('jax_platform_name', 'cpu')\n",
+    "from jax.experimental import optimizers\n",
     "import jax.numpy as np\n",
     "\n",
+    "from numpyro.contrib.autoguide import AutoIAFNormal\n",
     "import numpyro.distributions as dist\n",
     "from numpyro.examples.datasets import COVTYPE, load_dataset\n",
     "from numpyro.handlers import sample, scale, seed, substitute, trace\n",
     "from numpyro.hmc_util import consensus, initialize_model, parametric_draws\n",
-    "from numpyro.mcmc import mcmc"
+    "from numpyro.mcmc import mcmc\n",
+    "from numpyro.svi import elbo, svi"
    ]
   },
   {
@@ -96,11 +100,12 @@
     "    shards = []\n",
     "    for i in range(K):\n",
     "        shards.append((X[i * N: (i + 1) * N], y[i * N: (i + 1) * N]))\n",
+    "    train_data = (X[:K * N], y[:K * N])\n",
     "    test_data = (X[K * N:], y[K * N:])\n",
-    "    return shards, test_data\n",
+    "    return shards, train_data, test_data\n",
     "\n",
     "K, N = 40, 10000\n",
-    "shards, (X_test, y_test) = get_train_shards_and_test_data(\n",
+    "shards, (X_train, y_train), (X_test, y_test) = get_train_shards_and_test_data(\n",
     "    X_full, y_full, K, N, random.PRNGKey(0))\n",
     "print(\"Train set contains {} ({}%) data points.\".format(\n",
     "    K * N, round(K * N / X_full.shape[0] * 100, 2)))\n",
@@ -2679,13 +2684,81 @@
     "acc = (y_parametric == y_test).sum() / y_test.shape[0]\n",
     "print('Parametric accuaracy: {}'.format(round(acc.item(), 4)))"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### train iaf"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def model(X, y):\n",
+    "    coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
+    "    with scale(X_train.shape[0] / X.shape[0]):\n",
+    "        return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rng_guide, rng_init, rng_train = random.split(random.PRNGKey(3), 3)\n",
+    "opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
+    "guide = AutoIAFNormal(rng_guide, model, get_params)\n",
+    "svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params)\n",
+    "batch_size = 1000\n",
+    "num_epochs = 10\n",
+    "\n",
+    "def epoch_train(X, y, opt_state, rng):\n",
+    "    # shuffle data\n",
+    "    rng, rng_shuffle = random.split(rng)\n",
+    "    idx = random.shuffle(rng_shuffle, np.arange(X.shape[0]))\n",
+    "    X = X[idx]\n",
+    "    y = y[idx]\n",
+    "\n",
+    "    def body_fn(val, i):\n",
+    "        batch_X = lax.dynamic_slice_in_dim(X, i * batch_size, batch_size)\n",
+    "        batch_y = lax.dynamic_slice_in_dim(y, i * batch_size, batch_size)\n",
+    "        opt_state_, rng_ = val\n",
+    "        loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_,\n",
+    "                                            (batch_X, batch_y), (batch_X, batch_y))\n",
+    "        return (opt_state_, rng_), loss\n",
+    "\n",
+    "    (opt_state, _), losses = lax.scan(body_fn, (opt_state, rng),\n",
+    "                                      np.arange(X.shape[0] // batch_size))\n",
+    "    return opt_state, np.mean(losses)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "opt_state, _ = svi_init(rng_init,\n",
+    "                        (X_train[:batch_size], y_train[:batch_size]),\n",
+    "                        (X_train[:batch_size], y_train[:batch_size]))\n",
+    "\n",
+    "losses = []\n",
+    "for epoch in range(num_epochs):\n",
+    "    rng = random.fold_in(rng_train, epoch)\n",
+    "    opt_state, losses = epoch_train(X_train, y_train, opt_state, rng)"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python (test)",
+   "display_name": "Python (pydata)",
    "language": "python",
-   "name": "test"
+   "name": "pydata"
   },
   "language_info": {
    "codemirror_mode": {
@@ -2697,7 +2770,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.6.9"
   }
  },
  "nbformat": 4,

From c3a9438c08cbddab112fe53747b073b9bd6f1a09 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sat, 10 Aug 2019 16:05:40 -0400
Subject: [PATCH 21/35] add iaf result

---
 notebooks/source/covtype.ipynb | 271 +++++++++++++++++++++++++++++----
 1 file changed, 240 insertions(+), 31 deletions(-)

diff --git a/notebooks/source/covtype.ipynb b/notebooks/source/covtype.ipynb
index 8d3982e5c..51180dcfc 100644
--- a/notebooks/source/covtype.ipynb
+++ b/notebooks/source/covtype.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -79,7 +79,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -122,14 +122,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def model(X, y, K=1):\n",
-    "    with scale(1 / K):\n",
+    "def model(X, y, prior_scale=1, likelihood_scale=1):\n",
+    "    with scale(prior_scale):\n",
     "        coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
-    "    return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
+    "    with scale(likelihood_scale):\n",
+    "        return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
    ]
   },
   {
@@ -148,7 +149,7 @@
     "def get_subposterior(rng, shard, K):\n",
     "    rngs = random.split(rng, 4)\n",
     "    X, y = shard\n",
-    "    init_params, potential_fn, _ = initialize_model(rngs, model, X, y, K=K)\n",
+    "    init_params, potential_fn, _ = initialize_model(rngs, model, X, y, prior_scale=1 / K)\n",
     "    samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
     "                   num_chains=4, potential_fn=potential_fn)\n",
     "    return samples"
@@ -2647,7 +2648,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2694,64 +2695,272 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def model(X, y):\n",
-    "    coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
-    "    with scale(X_train.shape[0] / X.shape[0]):\n",
-    "        return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
+    "from jax.experimental import stax"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 56,
    "metadata": {},
    "outputs": [],
    "source": [
     "rng_guide, rng_init, rng_train = random.split(random.PRNGKey(3), 3)\n",
     "opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
-    "guide = AutoIAFNormal(rng_guide, model, get_params)\n",
-    "svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params)\n",
+    "guide = AutoIAFNormal(rng_guide, model, get_params, nonlinearity=stax.Elu,\n",
+    "                      skip_connections=False)\n",
+    "ll_scale = X_train.shape[0] // batch_size\n",
+    "svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params,\n",
+    "                              likelihood_scale=ll_scale)\n",
     "batch_size = 1000\n",
-    "num_epochs = 10\n",
+    "num_iters = ll_scale\n",
     "\n",
-    "def epoch_train(X, y, opt_state, rng):\n",
+    "def epoch_train(epoch, opt_state, rng):\n",
     "    # shuffle data\n",
     "    rng, rng_shuffle = random.split(rng)\n",
-    "    idx = random.shuffle(rng_shuffle, np.arange(X.shape[0]))\n",
-    "    X = X[idx]\n",
-    "    y = y[idx]\n",
+    "    idx = random.shuffle(rng_shuffle, np.arange(X_train.shape[0]))\n",
+    "    X = X_train[idx]\n",
+    "    y = y_train[idx]\n",
+    "    offset = epoch * num_iters\n",
     "\n",
     "    def body_fn(val, i):\n",
     "        batch_X = lax.dynamic_slice_in_dim(X, i * batch_size, batch_size)\n",
     "        batch_y = lax.dynamic_slice_in_dim(y, i * batch_size, batch_size)\n",
     "        opt_state_, rng_ = val\n",
-    "        loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_,\n",
+    "        loss, opt_state_, rng_ = svi_update(offset + i, rng_, opt_state_,\n",
     "                                            (batch_X, batch_y), (batch_X, batch_y))\n",
     "        return (opt_state_, rng_), loss\n",
     "\n",
-    "    (opt_state, _), losses = lax.scan(body_fn, (opt_state, rng),\n",
-    "                                      np.arange(X.shape[0] // batch_size))\n",
-    "    return opt_state, np.mean(losses)"
+    "    (opt_state, _), losses = lax.scan(body_fn, (opt_state, rng), np.arange(num_iters))\n",
+    "    return opt_state, losses"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 57,
    "metadata": {},
    "outputs": [],
    "source": [
     "opt_state, _ = svi_init(rng_init,\n",
     "                        (X_train[:batch_size], y_train[:batch_size]),\n",
-    "                        (X_train[:batch_size], y_train[:batch_size]))\n",
-    "\n",
-    "losses = []\n",
+    "                        (X_train[:batch_size], y_train[:batch_size]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 00 - loss 1883.5496 - acc 0.7612\n",
+      "Epoch 01 - loss 688.8702 - acc 0.7706\n",
+      "Epoch 02 - loss 617.3635 - acc 0.7685\n",
+      "Epoch 03 - loss 601.3757 - acc 0.7711\n",
+      "Epoch 04 - loss 598.3813 - acc 0.7687\n",
+      "Epoch 05 - loss 593.7759 - acc 0.7708\n",
+      "Epoch 06 - loss 593.0955 - acc 0.7692\n",
+      "Epoch 07 - loss 590.5724 - acc 0.7714\n",
+      "Epoch 08 - loss 589.2113 - acc 0.7693\n",
+      "Epoch 09 - loss 588.8226 - acc 0.7721\n"
+     ]
+    }
+   ],
+   "source": [
+    "losses = np.array([])\n",
+    "num_epochs = 10\n",
+    "rngs = random.split(random.PRNGKey(2), 10000)\n",
+    "for epoch in range(num_epochs):\n",
+    "    rng = random.fold_in(rng_train, epoch)\n",
+    "    opt_state, epoch_loss = epoch_train(epoch, opt_state, rng)\n",
+    "    iaf_samples = guide.sample_posterior(random.PRNGKey(4), opt_state, sample_shape=(10000,))\n",
+    "    y_iaf = vmap(partial(predict, model, X_test))(rngs, iaf_samples)\n",
+    "    y_iaf = (y_iaf.sum(axis=0) / y_iaf.shape[0]) >= 0.5\n",
+    "    acc = (y_iaf == y_test).sum() / y_test.shape[0]\n",
+    "    print(\"Epoch {:02d} - loss {:.4f} - acc {}\".format(\n",
+    "        epoch, np.mean(epoch_loss), round(acc.item(), 4)))\n",
+    "    losses = np.concatenate([losses, epoch_loss])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 00 - loss 254534.3438 - acc 0.6719\n",
+      "Epoch 01 - loss 65498.4805 - acc 0.6963\n",
+      "Epoch 02 - loss 58030.9766 - acc 0.6833\n",
+      "Epoch 03 - loss 11353.0801 - acc 0.697\n",
+      "Epoch 04 - loss 10766.7871 - acc 0.7035\n",
+      "Epoch 05 - loss 5903.0508 - acc 0.6917\n",
+      "Epoch 06 - loss 4735.4136 - acc 0.7204\n",
+      "Epoch 07 - loss 3767.8457 - acc 0.7249\n",
+      "Epoch 08 - loss 2702.3569 - acc 0.7115\n",
+      "Epoch 09 - loss 4246.7715 - acc 0.7243\n",
+      "Epoch 10 - loss 2887.8103 - acc 0.7419\n",
+      "Epoch 11 - loss 1575.2468 - acc 0.7423\n",
+      "Epoch 12 - loss 3265.4502 - acc 0.7482\n",
+      "Epoch 13 - loss 1635.4376 - acc 0.7575\n",
+      "Epoch 14 - loss 2030.9865 - acc 0.7576\n",
+      "Epoch 15 - loss 1211.5005 - acc 0.747\n",
+      "Epoch 16 - loss 1234.9969 - acc 0.7586\n",
+      "Epoch 17 - loss 1120.3951 - acc 0.7628\n",
+      "Epoch 18 - loss 1038.1304 - acc 0.7655\n",
+      "Epoch 19 - loss 1188.7095 - acc 0.7434\n",
+      "Epoch 20 - loss 1023.7824 - acc 0.7597\n",
+      "Epoch 21 - loss 1024.2365 - acc 0.7727\n",
+      "Epoch 22 - loss 1002.4470 - acc 0.759\n",
+      "Epoch 23 - loss 1038.4382 - acc 0.768\n",
+      "Epoch 24 - loss 940.9832 - acc 0.7611\n",
+      "Epoch 25 - loss 895.9312 - acc 0.7674\n",
+      "Epoch 26 - loss 1345.1897 - acc 0.7639\n",
+      "Epoch 27 - loss 917.5681 - acc 0.76\n",
+      "Epoch 28 - loss 934.0630 - acc 0.7578\n",
+      "Epoch 29 - loss 881.1840 - acc 0.7477\n",
+      "Epoch 30 - loss 945.5895 - acc 0.7615\n",
+      "Epoch 31 - loss 881.6766 - acc 0.7651\n",
+      "Epoch 32 - loss 856.6132 - acc 0.7531\n",
+      "Epoch 33 - loss 977.1152 - acc 0.7651\n",
+      "Epoch 34 - loss 860.5390 - acc 0.757\n",
+      "Epoch 35 - loss 860.3196 - acc 0.7687\n",
+      "Epoch 36 - loss 841.2369 - acc 0.7647\n",
+      "Epoch 37 - loss 851.6643 - acc 0.7592\n",
+      "Epoch 38 - loss 813.6900 - acc 0.7679\n",
+      "Epoch 39 - loss 812.2313 - acc 0.7544\n",
+      "Epoch 40 - loss 808.4932 - acc 0.7634\n",
+      "Epoch 41 - loss 886.4514 - acc 0.7698\n",
+      "Epoch 42 - loss 817.3934 - acc 0.7537\n",
+      "Epoch 43 - loss 789.4904 - acc 0.7707\n",
+      "Epoch 44 - loss 790.3774 - acc 0.7612\n",
+      "Epoch 45 - loss 770.7787 - acc 0.7664\n",
+      "Epoch 46 - loss 764.3374 - acc 0.7694\n",
+      "Epoch 47 - loss 742.7781 - acc 0.7739\n",
+      "Epoch 48 - loss 734.4012 - acc 0.7643\n",
+      "Epoch 49 - loss 725.6569 - acc 0.7688\n",
+      "Epoch 50 - loss 713.1312 - acc 0.7696\n",
+      "Epoch 51 - loss 702.3688 - acc 0.7701\n",
+      "Epoch 52 - loss 694.8310 - acc 0.768\n",
+      "Epoch 53 - loss 690.0838 - acc 0.7679\n",
+      "Epoch 54 - loss 680.3116 - acc 0.7689\n",
+      "Epoch 55 - loss 688.9963 - acc 0.7622\n",
+      "Epoch 56 - loss 671.6235 - acc 0.7716\n",
+      "Epoch 57 - loss 661.0634 - acc 0.7642\n",
+      "Epoch 58 - loss 654.5287 - acc 0.7706\n",
+      "Epoch 59 - loss 719.4338 - acc 0.7696\n",
+      "Epoch 60 - loss 667.0007 - acc 0.7694\n",
+      "Epoch 61 - loss 649.3066 - acc 0.7701\n",
+      "Epoch 62 - loss 639.6379 - acc 0.7712\n",
+      "Epoch 63 - loss 634.2900 - acc 0.7695\n",
+      "Epoch 64 - loss 630.7141 - acc 0.7666\n",
+      "Epoch 65 - loss 628.7311 - acc 0.7717\n",
+      "Epoch 66 - loss 622.4650 - acc 0.7671\n",
+      "Epoch 67 - loss 619.6395 - acc 0.7696\n",
+      "Epoch 68 - loss 618.3934 - acc 0.7711\n",
+      "Epoch 69 - loss 613.0114 - acc 0.7702\n",
+      "Epoch 70 - loss 613.1573 - acc 0.7714\n",
+      "Epoch 71 - loss 608.6863 - acc 0.7656\n",
+      "Epoch 72 - loss 603.2803 - acc 0.7718\n",
+      "Epoch 73 - loss 604.5390 - acc 0.7671\n",
+      "Epoch 74 - loss 599.7892 - acc 0.7716\n",
+      "Epoch 75 - loss 598.3097 - acc 0.7695\n",
+      "Epoch 76 - loss 597.3398 - acc 0.77\n",
+      "Epoch 77 - loss 592.6534 - acc 0.7698\n",
+      "Epoch 78 - loss 590.7097 - acc 0.7686\n",
+      "Epoch 79 - loss 590.5514 - acc 0.7692\n",
+      "Epoch 80 - loss 588.7484 - acc 0.7694\n",
+      "Epoch 81 - loss 589.0543 - acc 0.7723\n",
+      "Epoch 82 - loss 586.3735 - acc 0.7697\n",
+      "Epoch 83 - loss 589.2031 - acc 0.7659\n",
+      "Epoch 84 - loss 587.5204 - acc 0.7697\n",
+      "Epoch 85 - loss 586.9933 - acc 0.7679\n",
+      "Epoch 86 - loss 586.1766 - acc 0.7689\n",
+      "Epoch 87 - loss 584.0955 - acc 0.7702\n",
+      "Epoch 88 - loss 584.7559 - acc 0.7699\n",
+      "Epoch 89 - loss 583.4180 - acc 0.7715\n",
+      "Epoch 90 - loss 583.9426 - acc 0.7715\n",
+      "Epoch 91 - loss 582.8043 - acc 0.7687\n",
+      "Epoch 92 - loss 582.0665 - acc 0.7677\n",
+      "Epoch 93 - loss 582.5842 - acc 0.7703\n",
+      "Epoch 94 - loss 583.2501 - acc 0.7711\n",
+      "Epoch 95 - loss 582.0706 - acc 0.7708\n",
+      "Epoch 96 - loss 581.0920 - acc 0.77\n",
+      "Epoch 97 - loss 581.4358 - acc 0.7716\n",
+      "Epoch 98 - loss 582.6833 - acc 0.7713\n",
+      "Epoch 99 - loss 581.7660 - acc 0.7716\n"
+     ]
+    }
+   ],
+   "source": [
+    "losses = np.array([])\n",
+    "num_epochs = 100\n",
+    "rngs = random.split(random.PRNGKey(2), 10000)\n",
     "for epoch in range(num_epochs):\n",
     "    rng = random.fold_in(rng_train, epoch)\n",
-    "    opt_state, losses = epoch_train(X_train, y_train, opt_state, rng)"
+    "    opt_state, epoch_loss = epoch_train(epoch, opt_state, rng)\n",
+    "    iaf_samples = guide.sample_posterior(random.PRNGKey(4), opt_state, sample_shape=(10000,))\n",
+    "    y_iaf = vmap(partial(predict, model, X_test))(rngs, iaf_samples)\n",
+    "    y_iaf = (y_iaf.sum(axis=0) / y_iaf.shape[0]) >= 0.5\n",
+    "    acc = (y_iaf == y_test).sum() / y_test.shape[0]\n",
+    "    print(\"Epoch {:02d} - loss {:.4f} - acc {}\".format(\n",
+    "        epoch, np.mean(epoch_loss), round(acc.item(), 4)))\n",
+    "    losses = np.concatenate([losses, epoch_loss])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Flow HMC"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "transform = guide.get_transform(opt_state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "unpack_fn = guide.unpack_latent"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def make_transformed_pe(potential_fn, transform, unpack_fn):\n",
+    "    def transformed_potential_fn(z):\n",
+    "        u, intermediates = transform.call_with_intermediates(z)\n",
+    "        logdet = transform.log_abs_det_jacobian(z, u, intermediates=intermediates)\n",
+    "        return potential_fn(unpack_fn(u)) + logdet\n",
+    "\n",
+    "    return transformed_potential_fn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -2774,5 +2983,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }

From 493ca87828c3f272b38ab3a75be929cda0a72b75 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sun, 11 Aug 2019 02:52:10 -0400
Subject: [PATCH 22/35] temp delete

---
 notebooks/source/covtype.ipynb | 2987 --------------------------------
 1 file changed, 2987 deletions(-)
 delete mode 100644 notebooks/source/covtype.ipynb

diff --git a/notebooks/source/covtype.ipynb b/notebooks/source/covtype.ipynb
deleted file mode 100644
index 51180dcfc..000000000
--- a/notebooks/source/covtype.ipynb
+++ /dev/null
@@ -1,2987 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from functools import partial\n",
-    "import os; os.environ['XLA_FLAGS'] = '--xla_force_host_platform_device_count=4'\n",
-    "\n",
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as onp\n",
-    "\n",
-    "from jax import jit, lax, random, vmap\n",
-    "from jax.config import config; config.update('jax_platform_name', 'cpu')\n",
-    "from jax.experimental import optimizers\n",
-    "import jax.numpy as np\n",
-    "\n",
-    "from numpyro.contrib.autoguide import AutoIAFNormal\n",
-    "import numpyro.distributions as dist\n",
-    "from numpyro.examples.datasets import COVTYPE, load_dataset\n",
-    "from numpyro.handlers import sample, scale, seed, substitute, trace\n",
-    "from numpyro.hmc_util import consensus, initialize_model, parametric_draws\n",
-    "from numpyro.mcmc import mcmc\n",
-    "from numpyro.svi import elbo, svi"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### load data"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Data shape: (581012, 55)\n",
-      "Label distribution: 211840 has label 1, 369172 has label 0\n"
-     ]
-    }
-   ],
-   "source": [
-    "def _load_dataset():\n",
-    "    _, fetch = load_dataset(COVTYPE, shuffle=False)\n",
-    "    features, labels = fetch()\n",
-    "\n",
-    "    # normalize features and add intercept\n",
-    "    features = (features - features.mean(0)) / features.std(0)\n",
-    "    features = np.hstack([features, np.ones((features.shape[0], 1))])\n",
-    "\n",
-    "    # make binary feature\n",
-    "    _, counts = onp.unique(labels, return_counts=True)\n",
-    "    specific_category = np.argmax(counts)\n",
-    "    labels = (labels == specific_category)\n",
-    "\n",
-    "    N, dim = features.shape\n",
-    "    print(\"Data shape:\", features.shape)\n",
-    "    print(\"Label distribution: {} has label 1, {} has label 0\"\n",
-    "          .format(labels.sum(), N - labels.sum()))\n",
-    "    return features, labels\n",
-    "\n",
-    "X_full, y_full = _load_dataset()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### prepare train shards and test set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Train set contains 400000 (68.85%) data points.\n",
-      "Test set contains 181012 (31.15%) data points.\n"
-     ]
-    }
-   ],
-   "source": [
-    "def get_train_shards_and_test_data(X, y, K, N, rng=None):\n",
-    "    if rng is not None:\n",
-    "        idxs = random.shuffle(rng, np.arange(X.shape[0]))\n",
-    "        X = X[idxs]\n",
-    "        y = y[idxs]\n",
-    "    shards = []\n",
-    "    for i in range(K):\n",
-    "        shards.append((X[i * N: (i + 1) * N], y[i * N: (i + 1) * N]))\n",
-    "    train_data = (X[:K * N], y[:K * N])\n",
-    "    test_data = (X[K * N:], y[K * N:])\n",
-    "    return shards, train_data, test_data\n",
-    "\n",
-    "K, N = 40, 10000\n",
-    "shards, (X_train, y_train), (X_test, y_test) = get_train_shards_and_test_data(\n",
-    "    X_full, y_full, K, N, random.PRNGKey(0))\n",
-    "print(\"Train set contains {} ({}%) data points.\".format(\n",
-    "    K * N, round(K * N / X_full.shape[0] * 100, 2)))\n",
-    "print(\"Test set contains {} ({}%) data points.\".format(\n",
-    "    X_full.shape[0] - K * N, round(100 - K * N / X_full.shape[0] * 100, 2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### model"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def model(X, y, prior_scale=1, likelihood_scale=1):\n",
-    "    with scale(prior_scale):\n",
-    "        coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
-    "    with scale(likelihood_scale):\n",
-    "        return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### sampling"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def get_subposterior(rng, shard, K):\n",
-    "    rngs = random.split(rng, 4)\n",
-    "    X, y = shard\n",
-    "    init_params, potential_fn, _ = initialize_model(rngs, model, X, y, prior_scale=1 / K)\n",
-    "    samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
-    "                   num_chains=4, potential_fn=potential_fn)\n",
-    "    return samples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      " =============================== SUBPOSTERIOR 00 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.94      0.06      1.94      1.84      2.04  10596.19      1.00\n",
-      "  coefs[1]      0.00      0.03      0.00     -0.06      0.06  13018.15      1.00\n",
-      "  coefs[2]     -0.05      0.07     -0.05     -0.15      0.06   3962.76      1.00\n",
-      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   8349.60      1.00\n",
-      "  coefs[4]     -0.13      0.04     -0.13     -0.19     -0.07   9673.05      1.00\n",
-      "  coefs[5]     -0.09      0.03     -0.09     -0.15     -0.04  11774.95      1.00\n",
-      "  coefs[6]      0.33      0.25      0.32     -0.08      0.73   3044.25      1.00\n",
-      "  coefs[7]     -0.70      0.15     -0.69     -0.94     -0.45   3230.34      1.00\n",
-      "  coefs[8]      0.61      0.29      0.60      0.12      1.08   3048.04      1.00\n",
-      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.01  11912.89      1.00\n",
-      " coefs[10]      0.38      0.65      0.37     -0.66      1.50   3045.41      1.00\n",
-      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.42   3041.88      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -0.99      1.17   3040.15      1.00\n",
-      " coefs[13]     -0.94      0.65     -0.88     -2.00      0.08   5089.97      1.00\n",
-      " coefs[14]     -0.48      0.67     -0.37     -1.51      0.56   5935.95      1.00\n",
-      " coefs[15]     -0.80      0.56     -0.69     -1.65      0.03   5174.92      1.00\n",
-      " coefs[16]     -0.71      0.60     -0.59     -1.63      0.11   4779.67      1.00\n",
-      " coefs[17]     -0.28      0.22     -0.27     -0.65      0.08   1027.92      1.00\n",
-      " coefs[18]     -0.57      0.66     -0.46     -1.58      0.40   5873.46      1.00\n",
-      " coefs[19]     -0.49      0.67     -0.39     -1.61      0.53   5699.48      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.03   5339.04      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1357.53      1.00\n",
-      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11   1117.18      1.00\n",
-      " coefs[23]     -0.07      0.25     -0.07     -0.47      0.34    537.29      1.00\n",
-      " coefs[24]     -0.04      0.16     -0.04     -0.31      0.21    542.14      1.00\n",
-      " coefs[25]     -0.01      0.23     -0.02     -0.39      0.35    498.36      1.00\n",
-      " coefs[26]     -0.01      0.18     -0.01     -0.31      0.27    506.74      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.12   5016.54      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.59      1.71  11735.13      1.00\n",
-      " coefs[29]      0.09      0.08      0.09     -0.04      0.21    522.46      1.00\n",
-      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    581.10      1.00\n",
-      " coefs[31]      0.04      0.08      0.04     -0.09      0.16    822.05      1.00\n",
-      " coefs[32]      0.11      0.09      0.11     -0.03      0.26    518.96      1.00\n",
-      " coefs[33]      0.13      0.13      0.13     -0.08      0.34    494.96      1.00\n",
-      " coefs[34]      0.06      0.05      0.06     -0.02      0.15    858.21      1.00\n",
-      " coefs[35]      0.38      0.24      0.38     -0.01      0.77    488.03      1.00\n",
-      " coefs[36]      0.40      0.31      0.40     -0.10      0.90    484.06      1.00\n",
-      " coefs[37]      0.17      0.19      0.17     -0.13      0.50    491.13      1.00\n",
-      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05    833.97      1.00\n",
-      " coefs[39]     -0.01      0.08     -0.01     -0.14      0.11    601.79      1.00\n",
-      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    632.43      1.00\n",
-      " coefs[41]     -0.77      0.58     -0.65     -1.62      0.05   5172.22      1.00\n",
-      " coefs[42]      0.11      0.41      0.11     -0.56      0.77    485.90      1.00\n",
-      " coefs[43]     -0.04      0.23     -0.04     -0.40      0.34    487.10      1.00\n",
-      " coefs[44]      0.16      0.21      0.16     -0.19      0.50    486.21      1.00\n",
-      " coefs[45]      0.12      0.30      0.12     -0.36      0.61    485.58      1.00\n",
-      " coefs[46]      0.20      0.28      0.20     -0.26      0.64    488.71      1.00\n",
-      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    688.12      1.00\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    530.56      1.00\n",
-      " coefs[49]      0.02      1.00      0.01     -1.59      1.68  11841.74      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4715.49      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.17    496.97      1.00\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    491.79      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    498.09      1.00\n",
-      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4068.47      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 01 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.03      0.06      2.03      1.93      2.13   6297.01      1.00\n",
-      "  coefs[1]     -0.10      0.03     -0.10     -0.16     -0.05   6696.79      1.00\n",
-      "  coefs[2]     -0.04      0.07     -0.04     -0.16      0.09   2407.61      1.00\n",
-      "  coefs[3]     -0.23      0.03     -0.24     -0.29     -0.18   5620.77      1.00\n",
-      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   5804.19      1.00\n",
-      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13   6953.33      1.00\n",
-      "  coefs[6]      0.23      0.30      0.23     -0.26      0.72   2060.03      1.00\n",
-      "  coefs[7]     -0.64      0.18     -0.64     -0.94     -0.34   2165.40      1.00\n",
-      "  coefs[8]      0.68      0.35      0.67      0.11      1.27   2051.67      1.00\n",
-      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.02   7364.88      1.00\n",
-      " coefs[10]      0.42      0.65      0.42     -0.69      1.45   2455.62      1.00\n",
-      " coefs[11]     -0.05      0.29     -0.05     -0.54      0.41   2496.49      1.00\n",
-      " coefs[12]      0.07      0.65      0.06     -1.06      1.08   2474.35      1.00\n",
-      " coefs[13]     -1.02      0.64     -0.97     -2.04      0.02   3633.72      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.36     -1.51      0.55   3974.22      1.00\n",
-      " coefs[15]     -0.78      0.56     -0.68     -1.61      0.05   3326.03      1.00\n",
-      " coefs[16]     -0.74      0.58     -0.63     -1.61      0.10   3931.39      1.00\n",
-      " coefs[17]     -0.11      0.18     -0.10     -0.41      0.20    716.27      1.01\n",
-      " coefs[18]     -0.54      0.67     -0.44     -1.55      0.44   4309.01      1.00\n",
-      " coefs[19]     -0.44      0.68     -0.35     -1.56      0.59   4171.46      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   3801.33      1.00\n",
-      " coefs[21]      0.03      0.03      0.03     -0.01      0.07    928.09      1.00\n",
-      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    821.22      1.01\n",
-      " coefs[23]      0.03      0.24      0.04     -0.38      0.40    486.42      1.01\n",
-      " coefs[24]      0.05      0.15      0.05     -0.20      0.29    508.69      1.01\n",
-      " coefs[25]     -0.08      0.23     -0.08     -0.43      0.31    474.61      1.01\n",
-      " coefs[26]      0.01      0.18      0.02     -0.27      0.31    482.02      1.01\n",
-      " coefs[27]     -0.68      0.63     -0.56     -1.60      0.18   3544.17      1.00\n",
-      " coefs[28]     -0.78      0.60     -0.66     -1.60      0.03   3720.32      1.00\n",
-      " coefs[29]      0.09      0.08      0.09     -0.03      0.21    525.53      1.01\n",
-      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    779.43      1.01\n",
-      " coefs[31]     -0.04      0.10     -0.03     -0.19      0.11   1169.81      1.00\n",
-      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    512.40      1.01\n",
-      " coefs[33]      0.15      0.13      0.15     -0.05      0.37    482.55      1.01\n",
-      " coefs[34]      0.93      0.59      0.82      0.11      1.79   3574.15      1.00\n",
-      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    473.55      1.01\n",
-      " coefs[36]      0.30      0.30      0.30     -0.21      0.78    470.35      1.01\n",
-      " coefs[37]      0.17      0.19      0.17     -0.16      0.47    467.05      1.01\n",
-      " coefs[38]     -0.04      0.04     -0.04     -0.11      0.02    769.86      1.01\n",
-      " coefs[39]      0.01      0.08      0.01     -0.11      0.14    578.20      1.01\n",
-      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.08    612.50      1.01\n",
-      " coefs[41]     -0.80      0.59     -0.67     -1.64      0.04   3531.23      1.00\n",
-      " coefs[42]      0.02      0.41      0.02     -0.64      0.68    469.07      1.01\n",
-      " coefs[43]      0.02      0.23      0.02     -0.35      0.39    472.51      1.01\n",
-      " coefs[44]      0.16      0.21      0.16     -0.19      0.49    471.76      1.01\n",
-      " coefs[45]      0.09      0.29      0.09     -0.40      0.55    469.03      1.01\n",
-      " coefs[46]      0.23      0.27      0.23     -0.22      0.67    471.88      1.01\n",
-      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.04    839.36      1.01\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    510.68      1.01\n",
-      " coefs[49]      0.03      1.01      0.03     -1.59      1.76   7599.21      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.72     -1.67     -0.07   3259.83      1.00\n",
-      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.12    472.94      1.01\n",
-      " coefs[52]     -0.15      0.16     -0.15     -0.40      0.11    473.82      1.01\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.03    488.46      1.01\n",
-      " coefs[54]     -1.64      0.18     -1.63     -1.94     -1.34   2819.50      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 02 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.97      0.06      1.97      1.87      2.07  10141.39      1.00\n",
-      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.01  11681.33      1.00\n",
-      "  coefs[2]      0.05      0.08      0.05     -0.08      0.18   3349.04      1.00\n",
-      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.22   8028.85      1.00\n",
-      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.06   9352.06      1.00\n",
-      "  coefs[5]     -0.13      0.03     -0.13     -0.18     -0.07  11348.87      1.00\n",
-      "  coefs[6]      0.80      0.32      0.80      0.28      1.32   2779.37      1.00\n",
-      "  coefs[7]     -1.06      0.19     -1.06     -1.37     -0.74   2899.08      1.00\n",
-      "  coefs[8]      1.32      0.37      1.32      0.71      1.93   2786.07      1.00\n",
-      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  12106.53      1.00\n",
-      " coefs[10]      0.45      0.65      0.44     -0.64      1.50   2853.02      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.39   2876.41      1.00\n",
-      " coefs[12]      0.13      0.65      0.13     -0.96      1.18   2851.32      1.00\n",
-      " coefs[13]     -1.08      0.62     -1.02     -2.08     -0.10   4547.27      1.00\n",
-      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.56   5752.40      1.00\n",
-      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.06   4399.13      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.59     -1.58      0.16   5696.39      1.00\n",
-      " coefs[17]     -0.14      0.19     -0.13     -0.44      0.18    742.08      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.43     -1.58      0.39   5940.96      1.00\n",
-      " coefs[19]     -0.44      0.68     -0.35     -1.54      0.62   5852.71      1.00\n",
-      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5257.50      1.00\n",
-      " coefs[21]     -0.76      0.58     -0.64     -1.60      0.03   5145.51      1.00\n",
-      " coefs[22]      0.03      0.08      0.03     -0.08      0.16   1171.01      1.00\n",
-      " coefs[23]      0.16      0.25      0.15     -0.26      0.57    534.48      1.00\n",
-      " coefs[24]      0.02      0.16      0.02     -0.25      0.28    535.89      1.00\n",
-      " coefs[25]     -0.15      0.24     -0.16     -0.56      0.23    527.60      1.00\n",
-      " coefs[26]      0.06      0.18      0.06     -0.25      0.36    526.14      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.59     -1.61      0.13   5205.52      1.00\n",
-      " coefs[28]      0.03      1.00      0.04     -1.61      1.65  10712.86      1.00\n",
-      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    607.37      1.00\n",
-      " coefs[30]     -0.00      0.10     -0.00     -0.16      0.15    652.04      1.00\n",
-      " coefs[31]     -0.02      0.10     -0.01     -0.17      0.13   1134.64      1.00\n",
-      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    535.91      1.00\n",
-      " coefs[33]      0.15      0.14      0.15     -0.08      0.36    527.35      1.00\n",
-      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4974.60      1.00\n",
-      " coefs[35]      0.38      0.25      0.38     -0.04      0.78    520.29      1.00\n",
-      " coefs[36]      0.37      0.32      0.37     -0.14      0.92    516.69      1.00\n",
-      " coefs[37]      0.18      0.20      0.17     -0.17      0.49    518.95      1.00\n",
-      " coefs[38]     -0.80      0.58     -0.68     -1.65     -0.01   5323.77      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    622.80      1.00\n",
-      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    571.08      1.01\n",
-      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1236.93      1.00\n",
-      " coefs[42]      0.07      0.43      0.07     -0.61      0.79    513.79      1.00\n",
-      " coefs[43]      0.01      0.24      0.01     -0.38      0.41    521.37      1.00\n",
-      " coefs[44]      0.16      0.22      0.16     -0.21      0.52    511.80      1.00\n",
-      " coefs[45]      0.08      0.31      0.08     -0.43      0.58    514.38      1.00\n",
-      " coefs[46]      0.23      0.29      0.23     -0.23      0.71    515.12      1.00\n",
-      " coefs[47]     -0.13      0.09     -0.13     -0.27      0.01   1051.75      1.00\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    574.66      1.00\n",
-      " coefs[49]     -0.80      0.59     -0.68     -1.63      0.02   5085.05      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.07   4703.61      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.17    522.50      1.00\n",
-      " coefs[52]     -0.08      0.16     -0.07     -0.34      0.20    518.37      1.00\n",
-      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    526.44      1.00\n",
-      " coefs[54]     -1.67      0.19     -1.65     -1.95     -1.36   3894.03      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 03 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9308.68      1.00\n",
-      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.04  11831.11      1.00\n",
-      "  coefs[2]     -0.08      0.06     -0.08     -0.18      0.03   3625.92      1.00\n",
-      "  coefs[3]     -0.27      0.03     -0.27     -0.33     -0.22   7283.21      1.00\n",
-      "  coefs[4]     -0.09      0.03     -0.09     -0.14     -0.03   8157.44      1.00\n",
-      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10004.68      1.00\n",
-      "  coefs[6]      0.04      0.24      0.04     -0.35      0.44   2665.26      1.00\n",
-      "  coefs[7]     -0.57      0.15     -0.57     -0.80     -0.31   2781.87      1.00\n",
-      "  coefs[8]      0.33      0.28      0.33     -0.12      0.80   2642.32      1.00\n",
-      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11808.21      1.00\n",
-      " coefs[10]      0.37      0.65      0.37     -0.72      1.45   2985.63      1.00\n",
-      " coefs[11]     -0.00      0.29     -0.01     -0.48      0.49   2998.92      1.00\n",
-      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2991.93      1.00\n",
-      " coefs[13]     -0.99      0.63     -0.92     -1.99      0.04   4876.03      1.00\n",
-      " coefs[14]     -0.47      0.67     -0.36     -1.53      0.50   5544.85      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.06   4454.60      1.00\n",
-      " coefs[16]     -0.71      0.59     -0.60     -1.61      0.13   4989.00      1.00\n",
-      " coefs[17]      0.05      0.17      0.05     -0.23      0.32    633.85      1.00\n",
-      " coefs[18]     -0.54      0.66     -0.42     -1.54      0.43   5998.03      1.00\n",
-      " coefs[19]     -0.45      0.68     -0.35     -1.52      0.63   5489.12      1.00\n",
-      " coefs[20]     -0.77      0.58     -0.65     -1.61      0.02   5007.75      1.00\n",
-      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1821.60      1.00\n",
-      " coefs[22]     -0.00      0.08      0.00     -0.13      0.11   1044.03      1.00\n",
-      " coefs[23]      0.02      0.26      0.02     -0.40      0.45    600.96      1.00\n",
-      " coefs[24]      0.01      0.16      0.01     -0.24      0.30    591.14      1.00\n",
-      " coefs[25]     -0.05      0.24     -0.05     -0.45      0.34    569.65      1.00\n",
-      " coefs[26]     -0.00      0.19     -0.00     -0.29      0.33    572.75      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   4787.94      1.00\n",
-      " coefs[28]      0.03      0.99      0.04     -1.57      1.67   9415.44      1.00\n",
-      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    615.59      1.00\n",
-      " coefs[30]      0.03      0.10      0.03     -0.13      0.19    749.84      1.00\n",
-      " coefs[31]      0.01      0.08      0.01     -0.11      0.15    937.97      1.00\n",
-      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    585.50      1.00\n",
-      " coefs[33]      0.14      0.14      0.14     -0.08      0.37    578.11      1.00\n",
-      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1184.94      1.00\n",
-      " coefs[35]      0.34      0.25      0.34     -0.08      0.75    562.89      1.00\n",
-      " coefs[36]      0.36      0.32      0.36     -0.15      0.92    562.32      1.00\n",
-      " coefs[37]      0.16      0.20      0.16     -0.16      0.51    564.23      1.00\n",
-      " coefs[38]     -0.03      0.04     -0.03     -0.10      0.03    914.20      1.00\n",
-      " coefs[39]     -0.83      0.57     -0.71     -1.68     -0.05   4856.42      1.00\n",
-      " coefs[40]      0.09      0.05      0.09     -0.00      0.17    716.14      1.00\n",
-      " coefs[41]     -0.78      0.59     -0.66     -1.62      0.04   5147.75      1.00\n",
-      " coefs[42]      0.06      0.43      0.06     -0.63      0.80    560.74      1.00\n",
-      " coefs[43]      0.04      0.24      0.04     -0.36      0.44    567.24      1.00\n",
-      " coefs[44]      0.23      0.22      0.23     -0.14      0.59    562.82      1.00\n",
-      " coefs[45]      0.13      0.31      0.13     -0.38      0.65    562.89      1.00\n",
-      " coefs[46]      0.21      0.29      0.21     -0.26      0.69    560.89      1.00\n",
-      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.07    884.93      1.00\n",
-      " coefs[48]     -0.01      0.07     -0.01     -0.11      0.11    642.70      1.00\n",
-      " coefs[49]     -0.79      0.60     -0.67     -1.66      0.01   4636.00      1.00\n",
-      " coefs[50]     -0.85      0.59     -0.72     -1.68     -0.06   4578.95      1.00\n",
-      " coefs[51]     -0.07      0.18     -0.07     -0.36      0.22    573.25      1.00\n",
-      " coefs[52]     -0.11      0.17     -0.11     -0.39      0.15    567.32      1.00\n",
-      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.04    584.89      1.00\n",
-      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.43   3787.09      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 04 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9663.05      1.00\n",
-      "  coefs[1]      0.01      0.03      0.01     -0.04      0.07  12229.09      1.00\n",
-      "  coefs[2]     -0.05      0.08     -0.05     -0.18      0.08   3518.69      1.00\n",
-      "  coefs[3]     -0.27      0.03     -0.26     -0.32     -0.21   7811.88      1.00\n",
-      "  coefs[4]     -0.14      0.03     -0.14     -0.20     -0.09   8939.99      1.00\n",
-      "  coefs[5]     -0.21      0.03     -0.21     -0.26     -0.15  10756.10      1.00\n",
-      "  coefs[6]      0.29      0.32      0.28     -0.22      0.82   2819.50      1.00\n",
-      "  coefs[7]     -0.72      0.19     -0.72     -1.04     -0.41   2925.77      1.00\n",
-      "  coefs[8]      0.69      0.37      0.69      0.08      1.29   2825.15      1.00\n",
-      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  12007.14      1.00\n",
-      " coefs[10]      0.43      0.65      0.42     -0.67      1.47   3220.08      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3229.13      1.00\n",
-      " coefs[12]      0.10      0.65      0.09     -1.05      1.08   3214.88      1.00\n",
-      " coefs[13]     -1.04      0.62     -0.99     -2.05     -0.06   5156.93      1.00\n",
-      " coefs[14]     -0.45      0.68     -0.35     -1.52      0.56   5786.49      1.00\n",
-      " coefs[15]     -0.76      0.58     -0.65     -1.65      0.08   4260.86      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.61     -1.60      0.12   5213.66      1.00\n",
-      " coefs[17]     -0.04      0.17     -0.04     -0.31      0.23    558.39      1.00\n",
-      " coefs[18]     -0.52      0.68     -0.40     -1.59      0.44   6109.99      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.38     -1.58      0.58   5597.20      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5070.21      1.00\n",
-      " coefs[21]     -0.78      0.59     -0.66     -1.63      0.01   4634.14      1.00\n",
-      " coefs[22]      0.10      0.06      0.10      0.01      0.19    642.58      1.00\n",
-      " coefs[23]      0.12      0.24      0.11     -0.29      0.51    465.45      1.00\n",
-      " coefs[24]      0.09      0.15      0.09     -0.15      0.35    470.90      1.00\n",
-      " coefs[25]     -0.11      0.23     -0.11     -0.48      0.27    454.80      1.00\n",
-      " coefs[26]      0.00      0.18      0.00     -0.30      0.29    466.84      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   5204.11      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.60      1.66  11259.68      1.00\n",
-      " coefs[29]      0.09      0.08      0.08     -0.03      0.22    488.93      1.00\n",
-      " coefs[30]      0.02      0.09      0.03     -0.13      0.18    610.00      1.00\n",
-      " coefs[31]     -0.75      0.59     -0.63     -1.60      0.08   4911.00      1.00\n",
-      " coefs[32]      0.09      0.09      0.09     -0.05      0.23    463.51      1.00\n",
-      " coefs[33]      0.15      0.13      0.15     -0.06      0.37    460.50      1.00\n",
-      " coefs[34]      0.93      0.59      0.80      0.12      1.77   4713.75      1.00\n",
-      " coefs[35]      0.32      0.24      0.32     -0.07      0.72    450.32      1.00\n",
-      " coefs[36]      0.32      0.31      0.32     -0.19      0.82    446.76      1.00\n",
-      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    449.21      1.00\n",
-      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.02   1126.07      1.00\n",
-      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    542.39      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.03      0.12    514.96      1.00\n",
-      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1089.97      1.00\n",
-      " coefs[42]      0.05      0.41      0.05     -0.65      0.69    447.89      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.36      0.39    451.39      1.00\n",
-      " coefs[44]      0.18      0.21      0.18     -0.16      0.53    448.32      1.00\n",
-      " coefs[45]      0.12      0.30      0.12     -0.36      0.60    447.13      1.00\n",
-      " coefs[46]      0.20      0.28      0.20     -0.23      0.67    449.59      1.00\n",
-      " coefs[47]     -0.12      0.09     -0.11     -0.25      0.03    961.34      1.00\n",
-      " coefs[48]     -0.10      0.06     -0.10     -0.20      0.00    482.43      1.00\n",
-      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1292.54      1.00\n",
-      " coefs[50]     -0.84      0.58     -0.73     -1.68     -0.06   5019.30      1.00\n",
-      " coefs[51]     -0.09      0.17     -0.09     -0.36      0.19    453.50      1.00\n",
-      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.14    453.09      1.00\n",
-      " coefs[53]     -0.16      0.13     -0.16     -0.37      0.05    458.05      1.00\n",
-      " coefs[54]     -1.69      0.19     -1.68     -2.00     -1.40   4062.23      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 05 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.98      0.06      1.98      1.88      2.08  10055.48      1.00\n",
-      "  coefs[1]     -0.09      0.03     -0.09     -0.15     -0.03  13343.50      1.00\n",
-      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.06   3771.35      1.00\n",
-      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.20   8377.00      1.00\n",
-      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   9458.58      1.00\n",
-      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  11099.64      1.00\n",
-      "  coefs[6]      0.16      0.28      0.16     -0.28      0.65   2986.01      1.00\n",
-      "  coefs[7]     -0.68      0.17     -0.67     -0.95     -0.39   3098.70      1.00\n",
-      "  coefs[8]      0.53      0.33      0.53      0.01      1.08   2974.13      1.00\n",
-      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  12492.35      1.00\n",
-      " coefs[10]      0.43      0.65      0.42     -0.63      1.52   3281.51      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.05     -0.53      0.44   3280.68      1.00\n",
-      " coefs[12]      0.09      0.65      0.08     -0.95      1.20   3275.10      1.00\n",
-      " coefs[13]     -1.02      0.62     -0.96     -1.99      0.03   5048.16      1.00\n",
-      " coefs[14]     -0.45      0.66     -0.34     -1.48      0.55   6484.69      1.00\n",
-      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.07   4874.24      1.00\n",
-      " coefs[16]     -0.71      0.59     -0.59     -1.60      0.13   5196.60      1.00\n",
-      " coefs[17]     -0.85      0.54     -0.75     -1.71     -0.04   4288.80      1.00\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.42   5984.25      1.00\n",
-      " coefs[19]     -0.43      0.68     -0.34     -1.52      0.61   6184.44      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.61      0.02   5183.95      1.00\n",
-      " coefs[21]     -0.76      0.60     -0.65     -1.61      0.06   5107.29      1.00\n",
-      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    931.40      1.00\n",
-      " coefs[23]      0.12      0.25      0.12     -0.29      0.53    654.15      1.00\n",
-      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    661.51      1.00\n",
-      " coefs[25]      0.02      0.24      0.02     -0.38      0.39    640.94      1.00\n",
-      " coefs[26]      0.08      0.18      0.08     -0.22      0.38    650.77      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   5054.07      1.00\n",
-      " coefs[28]      0.02      1.00      0.02     -1.60      1.71  12236.32      1.00\n",
-      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    716.26      1.00\n",
-      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    819.35      1.00\n",
-      " coefs[31]     -0.76      0.58     -0.63     -1.63      0.05   5197.70      1.00\n",
-      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    664.44      1.00\n",
-      " coefs[33]      0.15      0.13      0.16     -0.07      0.37    636.44      1.00\n",
-      " coefs[34]      0.08      0.05      0.08      0.00      0.16    913.04      1.00\n",
-      " coefs[35]      0.38      0.25      0.38     -0.04      0.76    631.09      1.00\n",
-      " coefs[36]      0.41      0.32      0.42     -0.11      0.91    625.04      1.00\n",
-      " coefs[37]      0.16      0.20      0.17     -0.17      0.47    634.99      1.00\n",
-      " coefs[38]     -0.01      0.05     -0.01     -0.10      0.07   1734.43      1.00\n",
-      " coefs[39]      0.06      0.08      0.06     -0.07      0.18    733.19      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    751.19      1.00\n",
-      " coefs[41]     -0.77      0.58     -0.64     -1.64      0.04   5405.80      1.00\n",
-      " coefs[42]      0.13      0.42      0.13     -0.55      0.82    630.46      1.00\n",
-      " coefs[43]      0.06      0.24      0.07     -0.32      0.44    631.90      1.00\n",
-      " coefs[44]      0.19      0.22      0.19     -0.18      0.53    624.94      1.00\n",
-      " coefs[45]      0.17      0.30      0.17     -0.33      0.65    625.77      1.00\n",
-      " coefs[46]      0.25      0.28      0.25     -0.22      0.70    622.20      1.00\n",
-      " coefs[47]     -0.12      0.09     -0.12     -0.25      0.03   1352.86      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    690.67      1.00\n",
-      " coefs[49]      0.01      0.03      0.01     -0.04      0.06   2201.81      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.07   4536.52      1.00\n",
-      " coefs[51]     -0.07      0.17     -0.07     -0.36      0.19    638.33      1.00\n",
-      " coefs[52]     -0.06      0.16     -0.05     -0.32      0.21    633.89      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.08    644.18      1.00\n",
-      " coefs[54]     -1.83      0.20     -1.82     -2.15     -1.50   4430.47      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 06 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.95      0.06      1.95      1.85      2.05  10029.37      1.00\n",
-      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02  12149.78      1.00\n",
-      "  coefs[2]     -0.07      0.07     -0.07     -0.18      0.04   3538.75      1.00\n",
-      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.23   7831.87      1.00\n",
-      "  coefs[4]     -0.08      0.04     -0.08     -0.13     -0.02   8546.42      1.00\n",
-      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  11509.36      1.00\n",
-      "  coefs[6]      0.22      0.26      0.21     -0.20      0.65   2659.06      1.00\n",
-      "  coefs[7]     -0.68      0.16     -0.68     -0.94     -0.42   2786.69      1.00\n",
-      "  coefs[8]      0.62      0.30      0.61      0.14      1.13   2692.12      1.00\n",
-      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12142.73      1.00\n",
-      " coefs[10]      0.44      0.66      0.43     -0.66      1.52   3204.45      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.53      0.44   3207.91      1.00\n",
-      " coefs[12]      0.10      0.66      0.10     -1.00      1.17   3206.53      1.00\n",
-      " coefs[13]     -1.07      0.62     -1.02     -2.08     -0.09   4936.60      1.00\n",
-      " coefs[14]     -0.47      0.68     -0.35     -1.47      0.58   5590.17      1.00\n",
-      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.08   4904.63      1.00\n",
-      " coefs[16]     -0.73      0.57     -0.62     -1.60      0.10   5217.49      1.00\n",
-      " coefs[17]      0.01      0.16      0.01     -0.25      0.27    685.60      1.00\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.43   5794.67      1.00\n",
-      " coefs[19]     -0.45      0.68     -0.35     -1.55      0.59   5598.62      1.00\n",
-      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4899.15      1.00\n",
-      " coefs[21]     -0.79      0.59     -0.66     -1.64      0.01   4949.36      1.00\n",
-      " coefs[22]      0.05      0.05      0.05     -0.04      0.14    761.87      1.00\n",
-      " coefs[23]      0.13      0.24      0.13     -0.25      0.54    591.47      1.00\n",
-      " coefs[24]      0.13      0.15      0.13     -0.11      0.38    583.33      1.00\n",
-      " coefs[25]     -0.16      0.23     -0.16     -0.54      0.21    579.37      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.30    591.59      1.00\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.60      0.16   5125.28      1.00\n",
-      " coefs[28]      0.03      0.99      0.03     -1.60      1.64  11076.76      1.00\n",
-      " coefs[29]     -0.03      0.09     -0.03     -0.17      0.10    762.71      1.00\n",
-      " coefs[30]      0.05      0.09      0.05     -0.09      0.20    775.29      1.00\n",
-      " coefs[31]      0.01      0.08      0.01     -0.11      0.13    865.56      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.08      0.20    593.73      1.00\n",
-      " coefs[33]      0.14      0.13      0.14     -0.08      0.35    568.23      1.00\n",
-      " coefs[34]      0.11      0.05      0.10      0.03      0.19    939.36      1.00\n",
-      " coefs[35]      0.34      0.24      0.34     -0.04      0.73    567.29      1.00\n",
-      " coefs[36]      0.33      0.31      0.33     -0.16      0.83    557.88      1.00\n",
-      " coefs[37]      0.18      0.19      0.18     -0.12      0.50    561.91      1.00\n",
-      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.06    987.06      1.00\n",
-      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    660.49      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    719.50      1.00\n",
-      " coefs[41]     -0.78      0.58     -0.66     -1.62      0.03   5507.11      1.00\n",
-      " coefs[42]      0.02      0.41      0.02     -0.66      0.66    565.26      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    572.24      1.00\n",
-      " coefs[44]      0.17      0.21      0.17     -0.19      0.49    559.31      1.00\n",
-      " coefs[45]      0.13      0.29      0.13     -0.35      0.61    560.67      1.00\n",
-      " coefs[46]      0.23      0.27      0.24     -0.22      0.67    565.95      1.00\n",
-      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    932.54      1.00\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    626.56      1.00\n",
-      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4698.19      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4890.12      1.00\n",
-      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.11    581.16      1.00\n",
-      " coefs[52]     -0.12      0.16     -0.12     -0.37      0.13    576.92      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.07    586.00      1.00\n",
-      " coefs[54]     -1.69      0.18     -1.68     -1.98     -1.39   4293.06      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 07 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9250.39      1.00\n",
-      "  coefs[1]     -0.09      0.03     -0.09     -0.14     -0.03  11900.57      1.00\n",
-      "  coefs[2]     -0.07      0.06     -0.07     -0.18      0.03   3382.04      1.00\n",
-      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.25   7273.45      1.00\n",
-      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   8136.64      1.00\n",
-      "  coefs[5]     -0.08      0.03     -0.08     -0.14     -0.03  10454.22      1.00\n",
-      "  coefs[6]      0.18      0.25      0.17     -0.21      0.59   2678.54      1.00\n",
-      "  coefs[7]     -0.60      0.15     -0.60     -0.86     -0.37   2847.50      1.00\n",
-      "  coefs[8]      0.58      0.29      0.57      0.13      1.08   2654.20      1.00\n",
-      "  coefs[9]     -0.00      0.03     -0.00     -0.05      0.05  11135.80      1.00\n",
-      " coefs[10]      0.41      0.65      0.40     -0.64      1.49   2891.96      1.00\n",
-      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.40   2908.39      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -0.96      1.18   2906.43      1.00\n",
-      " coefs[13]     -1.06      0.62     -1.00     -1.98      0.01   4513.52      1.00\n",
-      " coefs[14]     -0.45      0.68     -0.33     -1.50      0.58   5874.76      1.00\n",
-      " coefs[15]     -0.80      0.56     -0.70     -1.69      0.00   4266.13      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.61     -1.61      0.10   5034.41      1.00\n",
-      " coefs[17]      0.03      0.17      0.03     -0.25      0.29    583.94      1.01\n",
-      " coefs[18]     -0.55      0.67     -0.42     -1.56      0.41   5785.31      1.00\n",
-      " coefs[19]     -0.45      0.68     -0.36     -1.58      0.56   5403.98      1.00\n",
-      " coefs[20]     -0.76      0.58     -0.65     -1.60      0.04   5347.55      1.00\n",
-      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1203.81      1.00\n",
-      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11    999.08      1.00\n",
-      " coefs[23]      0.18      0.25      0.19     -0.23      0.60    524.80      1.01\n",
-      " coefs[24]      0.08      0.16      0.08     -0.19      0.33    540.04      1.01\n",
-      " coefs[25]     -0.14      0.24     -0.14     -0.53      0.25    519.78      1.01\n",
-      " coefs[26]     -0.01      0.18     -0.01     -0.33      0.28    528.60      1.01\n",
-      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.15   5063.80      1.00\n",
-      " coefs[28]      0.03      0.99      0.03     -1.60      1.66  10397.30      1.00\n",
-      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    558.96      1.01\n",
-      " coefs[30]     -0.02      0.10     -0.02     -0.19      0.15    764.55      1.01\n",
-      " coefs[31]     -0.03      0.09     -0.03     -0.18      0.13   1073.59      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.10      0.20    533.20      1.01\n",
-      " coefs[33]      0.11      0.14      0.12     -0.10      0.34    521.92      1.01\n",
-      " coefs[34]      0.92      0.59      0.79      0.10      1.77   4646.56      1.00\n",
-      " coefs[35]      0.33      0.25      0.33     -0.08      0.73    510.92      1.01\n",
-      " coefs[36]      0.32      0.32      0.32     -0.22      0.83    510.46      1.01\n",
-      " coefs[37]      0.14      0.20      0.14     -0.21      0.45    510.92      1.01\n",
-      " coefs[38]     -0.07      0.05     -0.07     -0.15      0.01   1144.95      1.00\n",
-      " coefs[39]     -0.07      0.09     -0.07     -0.23      0.07    802.88      1.00\n",
-      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    590.70      1.01\n",
-      " coefs[41]     -0.78      0.59     -0.65     -1.65      0.04   4782.36      1.00\n",
-      " coefs[42]      0.05      0.42      0.05     -0.66      0.74    511.47      1.01\n",
-      " coefs[43]     -0.01      0.24     -0.01     -0.41      0.37    519.40      1.01\n",
-      " coefs[44]      0.16      0.22      0.17     -0.22      0.50    513.40      1.01\n",
-      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    510.38      1.01\n",
-      " coefs[46]      0.21      0.29      0.22     -0.27      0.67    508.85      1.01\n",
-      " coefs[47]     -0.85      0.57     -0.73     -1.66     -0.05   4640.92      1.00\n",
-      " coefs[48]     -0.06      0.07     -0.06     -0.17      0.04    567.66      1.01\n",
-      " coefs[49]     -0.80      0.59     -0.68     -1.65     -0.00   4733.44      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4562.81      1.00\n",
-      " coefs[51]     -0.14      0.17     -0.14     -0.42      0.15    524.03      1.01\n",
-      " coefs[52]     -0.06      0.16     -0.06     -0.33      0.21    517.19      1.01\n",
-      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.07    522.64      1.01\n",
-      " coefs[54]     -1.70      0.19     -1.69     -1.99     -1.39   3848.03      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 08 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.07      0.06      2.07      1.97      2.17   6006.90      1.00\n",
-      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02   6950.95      1.00\n",
-      "  coefs[2]     -0.02      0.07     -0.03     -0.15      0.10   2377.69      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   5572.29      1.00\n",
-      "  coefs[4]     -0.09      0.04     -0.09     -0.15     -0.03   5713.46      1.00\n",
-      "  coefs[5]     -0.17      0.03     -0.17     -0.22     -0.11   6679.18      1.00\n",
-      "  coefs[6]      0.41      0.30      0.40     -0.09      0.90   1949.82      1.00\n",
-      "  coefs[7]     -0.76      0.18     -0.75     -1.05     -0.45   2055.76      1.00\n",
-      "  coefs[8]      0.82      0.36      0.80      0.25      1.41   1971.61      1.00\n",
-      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04   7249.79      1.00\n",
-      " coefs[10]      0.42      0.67      0.41     -0.62      1.57   2239.69      1.00\n",
-      " coefs[11]     -0.09      0.30     -0.10     -0.58      0.39   2251.76      1.00\n",
-      " coefs[12]      0.11      0.67      0.10     -0.95      1.24   2239.80      1.00\n",
-      " coefs[13]     -0.98      0.63     -0.92     -1.95      0.06   3243.72      1.00\n",
-      " coefs[14]     -0.47      0.66     -0.37     -1.53      0.52   3707.25      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.67     -1.66      0.05   2946.07      1.00\n",
-      " coefs[16]     -0.73      0.59     -0.61     -1.60      0.13   3752.58      1.00\n",
-      " coefs[17]     -0.13      0.19     -0.13     -0.46      0.16    896.44      1.01\n",
-      " coefs[18]     -0.55      0.67     -0.43     -1.56      0.44   4189.47      1.00\n",
-      " coefs[19]     -0.43      0.68     -0.34     -1.49      0.64   4551.92      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.64     -1.62      0.03   3922.11      1.00\n",
-      " coefs[21]     -0.76      0.59     -0.63     -1.61      0.05   3791.52      1.00\n",
-      " coefs[22]      0.06      0.06      0.06     -0.03      0.16    903.58      1.01\n",
-      " coefs[23]      0.10      0.25      0.10     -0.31      0.52    635.36      1.01\n",
-      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    629.98      1.01\n",
-      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    618.53      1.01\n",
-      " coefs[26]      0.01      0.18      0.01     -0.30      0.30    621.07      1.01\n",
-      " coefs[27]     -0.70      0.62     -0.57     -1.61      0.16   3618.38      1.00\n",
-      " coefs[28]     -0.77      0.60     -0.65     -1.61      0.03   3809.29      1.00\n",
-      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    692.94      1.01\n",
-      " coefs[30]      0.11      0.09      0.11     -0.03      0.26    679.52      1.01\n",
-      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.07   3537.22      1.00\n",
-      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    646.89      1.01\n",
-      " coefs[33]      0.19      0.13      0.19     -0.03      0.41    619.62      1.01\n",
-      " coefs[34]      0.10      0.05      0.10      0.01      0.18    970.71      1.00\n",
-      " coefs[35]      0.35      0.25      0.35     -0.04      0.77    606.18      1.01\n",
-      " coefs[36]      0.38      0.32      0.37     -0.14      0.90    604.82      1.01\n",
-      " coefs[37]      0.18      0.20      0.18     -0.14      0.51    610.69      1.01\n",
-      " coefs[38]     -0.77      0.57     -0.66     -1.58      0.02   3904.29      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    724.62      1.01\n",
-      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    746.12      1.01\n",
-      " coefs[41]      0.04      0.06      0.04     -0.05      0.13    959.08      1.00\n",
-      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    605.63      1.01\n",
-      " coefs[43]      0.05      0.24      0.04     -0.33      0.44    609.63      1.01\n",
-      " coefs[44]      0.16      0.22      0.16     -0.20      0.52    605.83      1.01\n",
-      " coefs[45]      0.12      0.30      0.12     -0.40      0.60    602.34      1.01\n",
-      " coefs[46]      0.26      0.28      0.26     -0.21      0.72    603.36      1.01\n",
-      " coefs[47]     -0.08      0.07     -0.07     -0.19      0.04    976.89      1.00\n",
-      " coefs[48]     -0.12      0.06     -0.12     -0.23     -0.02    677.15      1.01\n",
-      " coefs[49]     -0.02      0.02     -0.02     -0.06      0.02   1377.67      1.00\n",
-      " coefs[50]     -0.84      0.58     -0.71     -1.66     -0.07   3162.14      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.39      0.17    616.19      1.01\n",
-      " coefs[52]     -0.11      0.16     -0.11     -0.39      0.15    615.73      1.01\n",
-      " coefs[53]     -0.13      0.13     -0.13     -0.35      0.08    625.27      1.01\n",
-      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   2716.86      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 09 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.01      0.06      2.01      1.91      2.12   9583.20      1.00\n",
-      "  coefs[1]     -0.02      0.03     -0.02     -0.08      0.03  12244.17      1.00\n",
-      "  coefs[2]      0.00      0.07      0.00     -0.11      0.12   3899.89      1.00\n",
-      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   7491.94      1.00\n",
-      "  coefs[4]     -0.06      0.03     -0.06     -0.11      0.00   8128.73      1.00\n",
-      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  11573.08      1.00\n",
-      "  coefs[6]      0.41      0.27      0.41     -0.01      0.87   3193.36      1.00\n",
-      "  coefs[7]     -0.72      0.16     -0.72     -0.99     -0.46   3342.76      1.00\n",
-      "  coefs[8]      0.74      0.31      0.74      0.22      1.25   3174.21      1.00\n",
-      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11291.83      1.00\n",
-      " coefs[10]      0.42      0.66      0.41     -0.66      1.50   3092.99      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.07     -0.55      0.41   3105.34      1.00\n",
-      " coefs[12]      0.08      0.66      0.07     -0.95      1.21   3098.35      1.00\n",
-      " coefs[13]     -0.98      0.63     -0.92     -2.01      0.04   4969.90      1.00\n",
-      " coefs[14]     -0.47      0.66     -0.37     -1.54      0.49   6361.60      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.66     -1.67      0.07   4862.64      1.00\n",
-      " coefs[16]     -0.69      0.58     -0.58     -1.56      0.15   5141.14      1.00\n",
-      " coefs[17]     -0.11      0.19     -0.10     -0.42      0.20    969.52      1.00\n",
-      " coefs[18]     -0.54      0.67     -0.42     -1.59      0.42   5803.27      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.38     -1.52      0.60   5673.56      1.00\n",
-      " coefs[20]      0.01      0.97      0.01     -1.58      1.61  11893.53      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1600.17      1.00\n",
-      " coefs[22]      0.13      0.05      0.13      0.04      0.21    754.02      1.00\n",
-      " coefs[23]      0.07      0.25      0.08     -0.35      0.47    676.30      1.00\n",
-      " coefs[24]      0.05      0.16      0.06     -0.21      0.31    649.22      1.00\n",
-      " coefs[25]     -0.07      0.24     -0.07     -0.45      0.32    638.48      1.00\n",
-      " coefs[26]      0.04      0.18      0.05     -0.26      0.34    635.07      1.00\n",
-      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.17   5073.59      1.00\n",
-      " coefs[28]      0.02      1.00      0.02     -1.61      1.64  10606.53      1.00\n",
-      " coefs[29]      0.07      0.08      0.08     -0.06      0.20    664.51      1.00\n",
-      " coefs[30]      0.02      0.10      0.02     -0.15      0.19    986.79      1.00\n",
-      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.08   4279.14      1.00\n",
-      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    654.63      1.00\n",
-      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    644.38      1.00\n",
-      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4721.10      1.00\n",
-      " coefs[35]      0.35      0.25      0.36     -0.05      0.76    626.40      1.00\n",
-      " coefs[36]      0.32      0.32      0.33     -0.23      0.81    621.11      1.00\n",
-      " coefs[37]      0.17      0.20      0.18     -0.17      0.49    620.09      1.00\n",
-      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    942.45      1.00\n",
-      " coefs[39]      0.05      0.07      0.05     -0.08      0.17    701.99      1.00\n",
-      " coefs[40]      0.04      0.05      0.04     -0.04      0.13    756.89      1.00\n",
-      " coefs[41]     -0.78      0.59     -0.65     -1.63      0.06   5097.00      1.00\n",
-      " coefs[42]      0.03      0.42      0.04     -0.69      0.70    616.88      1.00\n",
-      " coefs[43]      0.00      0.24      0.01     -0.39      0.39    616.74      1.00\n",
-      " coefs[44]      0.18      0.22      0.18     -0.19      0.53    626.94      1.00\n",
-      " coefs[45]      0.13      0.30      0.14     -0.38      0.62    622.26      1.00\n",
-      " coefs[46]      0.23      0.28      0.23     -0.25      0.69    622.08      1.00\n",
-      " coefs[47]     -0.09      0.09     -0.09     -0.23      0.05   1262.87      1.00\n",
-      " coefs[48]     -0.05      0.06     -0.05     -0.15      0.05    672.90      1.00\n",
-      " coefs[49]     -0.80      0.59     -0.69     -1.66     -0.01   4912.08      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4527.27      1.00\n",
-      " coefs[51]     -0.11      0.17     -0.11     -0.39      0.17    629.31      1.00\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.13    621.60      1.00\n",
-      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    630.94      1.00\n",
-      " coefs[54]     -1.72      0.19     -1.70     -2.04     -1.42   3986.73      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 10 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.87      0.06      1.87      1.77      1.97   9851.85      1.00\n",
-      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  12023.27      1.00\n",
-      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.03   3664.70      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8152.42      1.00\n",
-      "  coefs[4]     -0.11      0.03     -0.11     -0.17     -0.05   9085.34      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11119.98      1.00\n",
-      "  coefs[6]      0.03      0.25      0.02     -0.38      0.44   2855.36      1.00\n",
-      "  coefs[7]     -0.55      0.15     -0.54     -0.80     -0.30   3027.65      1.00\n",
-      "  coefs[8]      0.36      0.29      0.36     -0.12      0.83   2848.40      1.00\n",
-      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12091.31      1.00\n",
-      " coefs[10]      0.39      0.65      0.38     -0.70      1.43   3073.54      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.45   3091.90      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -0.96      1.17   3077.49      1.00\n",
-      " coefs[13]     -1.03      0.63     -0.97     -2.05     -0.03   5086.29      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.36     -1.52      0.54   5767.73      1.00\n",
-      " coefs[15]     -0.81      0.58     -0.70     -1.70      0.02   4429.92      1.00\n",
-      " coefs[16]     -0.75      0.58     -0.64     -1.62      0.10   5020.30      1.00\n",
-      " coefs[17]     -0.05      0.17     -0.05     -0.32      0.23    634.36      1.00\n",
-      " coefs[18]     -0.58      0.65     -0.47     -1.57      0.38   5653.50      1.00\n",
-      " coefs[19]     -0.49      0.68     -0.39     -1.57      0.56   5316.42      1.00\n",
-      " coefs[20]     -0.76      0.60     -0.64     -1.62      0.04   5141.74      1.00\n",
-      " coefs[21]      0.00      0.03      0.01     -0.04      0.06   1175.81      1.00\n",
-      " coefs[22]      0.09      0.05      0.09      0.00      0.17    589.10      1.00\n",
-      " coefs[23]      0.01      0.25      0.01     -0.39      0.42    537.95      1.00\n",
-      " coefs[24]     -0.03      0.16     -0.03     -0.29      0.23    562.57      1.00\n",
-      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.34    508.79      1.01\n",
-      " coefs[26]     -0.02      0.18     -0.02     -0.34      0.25    517.53      1.00\n",
-      " coefs[27]     -0.73      0.61     -0.61     -1.61      0.13   4770.04      1.00\n",
-      " coefs[28]      0.02      0.99      0.03     -1.55      1.72  10221.27      1.00\n",
-      " coefs[29]      0.04      0.08      0.04     -0.08      0.17    561.90      1.01\n",
-      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    748.10      1.00\n",
-      " coefs[31]     -0.01      0.08     -0.00     -0.13      0.12    783.81      1.00\n",
-      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    532.06      1.01\n",
-      " coefs[33]      0.17      0.13      0.17     -0.06      0.37    514.16      1.01\n",
-      " coefs[34]      0.90      0.60      0.78      0.08      1.75   4699.27      1.00\n",
-      " coefs[35]      0.28      0.24      0.28     -0.10      0.69    505.90      1.01\n",
-      " coefs[36]      0.33      0.31      0.34     -0.17      0.84    505.30      1.01\n",
-      " coefs[37]      0.16      0.19      0.16     -0.16      0.47    503.53      1.01\n",
-      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    827.64      1.00\n",
-      " coefs[39]     -0.03      0.08     -0.03     -0.16      0.11    663.60      1.00\n",
-      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    666.94      1.00\n",
-      " coefs[41]     -0.81      0.59     -0.68     -1.71     -0.03   4477.38      1.00\n",
-      " coefs[42]      0.06      0.41      0.07     -0.61      0.73    504.16      1.01\n",
-      " coefs[43]      0.03      0.23      0.04     -0.35      0.41    506.87      1.01\n",
-      " coefs[44]      0.20      0.21      0.20     -0.14      0.55    502.28      1.01\n",
-      " coefs[45]      0.08      0.30      0.09     -0.40      0.57    503.49      1.01\n",
-      " coefs[46]      0.17      0.28      0.18     -0.29      0.62    501.86      1.01\n",
-      " coefs[47]     -0.09      0.07     -0.08     -0.20      0.03    751.62      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    553.11      1.00\n",
-      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.01   4806.02      1.00\n",
-      " coefs[50]     -0.83      0.59     -0.70     -1.67     -0.03   4711.38      1.00\n",
-      " coefs[51]     -0.08      0.17     -0.08     -0.36      0.18    505.60      1.01\n",
-      " coefs[52]     -0.06      0.16     -0.06     -0.32      0.19    510.68      1.01\n",
-      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.01    515.18      1.01\n",
-      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.33   4089.82      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 11 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.92      0.06      1.92      1.82      2.02  10396.90      1.00\n",
-      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.03  11519.16      1.00\n",
-      "  coefs[2]     -0.06      0.06     -0.06     -0.16      0.04   4117.58      1.00\n",
-      "  coefs[3]     -0.29      0.03     -0.29     -0.35     -0.23   7737.34      1.00\n",
-      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8773.20      1.00\n",
-      "  coefs[5]     -0.17      0.03     -0.18     -0.22     -0.12  11016.25      1.00\n",
-      "  coefs[6]      0.19      0.21      0.18     -0.16      0.50   2829.57      1.00\n",
-      "  coefs[7]     -0.59      0.13     -0.58     -0.79     -0.38   3123.90      1.00\n",
-      "  coefs[8]      0.48      0.24      0.46      0.09      0.85   2830.52      1.00\n",
-      "  coefs[9]     -0.05      0.03     -0.05     -0.09      0.00  12268.23      1.00\n",
-      " coefs[10]      0.45      0.66      0.44     -0.64      1.53   3044.65      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.40   3052.36      1.00\n",
-      " coefs[12]      0.08      0.65      0.07     -1.01      1.15   3041.06      1.00\n",
-      " coefs[13]     -1.03      0.62     -0.97     -2.08     -0.06   4562.95      1.00\n",
-      " coefs[14]     -0.47      0.67     -0.35     -1.55      0.51   5903.18      1.00\n",
-      " coefs[15]     -0.80      0.56     -0.70     -1.67      0.02   4665.74      1.00\n",
-      " coefs[16]     -0.73      0.59     -0.62     -1.63      0.10   4957.23      1.00\n",
-      " coefs[17]      0.00      0.17      0.00     -0.27      0.28    610.13      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.41   5781.93      1.00\n",
-      " coefs[19]     -0.46      0.67     -0.37     -1.56      0.55   6074.50      1.00\n",
-      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.03   5252.85      1.00\n",
-      " coefs[21]     -0.00      0.03     -0.00     -0.05      0.05   1165.34      1.00\n",
-      " coefs[22]      0.05      0.05      0.06     -0.04      0.14    680.97      1.00\n",
-      " coefs[23]      0.09      0.25      0.10     -0.34      0.48    529.12      1.00\n",
-      " coefs[24]     -0.02      0.16     -0.01     -0.27      0.25    558.96      1.00\n",
-      " coefs[25]     -0.03      0.23     -0.02     -0.43      0.35    525.19      1.00\n",
-      " coefs[26]      0.06      0.18      0.07     -0.23      0.36    518.36      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.59     -1.62      0.13   4954.67      1.00\n",
-      " coefs[28]      0.02      0.99      0.03     -1.61      1.65  10846.53      1.00\n",
-      " coefs[29]      0.05      0.08      0.06     -0.08      0.18    563.62      1.00\n",
-      " coefs[30]     -0.05      0.10     -0.04     -0.22      0.11    807.13      1.00\n",
-      " coefs[31]     -0.76      0.58     -0.65     -1.62      0.03   4982.14      1.00\n",
-      " coefs[32]      0.09      0.09      0.10     -0.06      0.24    543.12      1.00\n",
-      " coefs[33]      0.14      0.13      0.14     -0.08      0.36    525.64      1.00\n",
-      " coefs[34]      0.16      0.06      0.15      0.06      0.26   1251.32      1.00\n",
-      " coefs[35]      0.38      0.25      0.39     -0.01      0.81    516.49      1.00\n",
-      " coefs[36]      0.34      0.31      0.35     -0.19      0.85    511.53      1.00\n",
-      " coefs[37]      0.19      0.20      0.19     -0.14      0.51    514.24      1.00\n",
-      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.05    703.70      1.00\n",
-      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    596.82      1.00\n",
-      " coefs[40]      0.06      0.05      0.06     -0.02      0.15    671.03      1.00\n",
-      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   4996.10      1.00\n",
-      " coefs[42]      0.08      0.42      0.09     -0.63      0.76    512.64      1.00\n",
-      " coefs[43]      0.00      0.23      0.01     -0.38      0.40    516.39      1.00\n",
-      " coefs[44]      0.18      0.22      0.18     -0.18      0.53    514.45      1.00\n",
-      " coefs[45]      0.15      0.30      0.16     -0.35      0.64    513.91      1.00\n",
-      " coefs[46]      0.23      0.28      0.24     -0.24      0.69    514.26      1.00\n",
-      " coefs[47]     -0.85      0.57     -0.72     -1.67     -0.04   4633.11      1.00\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    600.11      1.00\n",
-      " coefs[49]     -0.80      0.60     -0.68     -1.64      0.00   4628.84      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.09   4617.98      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.09     -0.40      0.17    524.69      1.00\n",
-      " coefs[52]     -0.12      0.16     -0.12     -0.40      0.14    525.01      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.09    532.74      1.00\n",
-      " coefs[54]     -1.74      0.19     -1.73     -2.04     -1.43   3929.35      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 12 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.04      0.06      2.04      1.93      2.14   8304.52      1.00\n",
-      "  coefs[1]     -0.01      0.04     -0.01     -0.06      0.06  10118.62      1.00\n",
-      "  coefs[2]     -0.12      0.07     -0.11     -0.24     -0.00   3682.19      1.00\n",
-      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   6963.70      1.00\n",
-      "  coefs[4]     -0.10      0.03     -0.10     -0.15     -0.04   7744.04      1.00\n",
-      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.09  10497.57      1.00\n",
-      "  coefs[6]      0.11      0.28      0.11     -0.34      0.58   2964.29      1.00\n",
-      "  coefs[7]     -0.58      0.17     -0.58     -0.85     -0.29   3083.36      1.00\n",
-      "  coefs[8]      0.40      0.33      0.39     -0.15      0.92   2948.26      1.00\n",
-      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  10148.21      1.00\n",
-      " coefs[10]      0.38      0.65      0.37     -0.72      1.41   3238.54      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3251.02      1.00\n",
-      " coefs[12]      0.11      0.65      0.11     -0.94      1.19   3237.31      1.00\n",
-      " coefs[13]     -1.00      0.63     -0.94     -2.09     -0.05   4687.49      1.00\n",
-      " coefs[14]     -0.44      0.67     -0.34     -1.50      0.56   6099.61      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.07   4550.37      1.00\n",
-      " coefs[16]     -0.71      0.58     -0.60     -1.61      0.12   4864.50      1.00\n",
-      " coefs[17]     -0.13      0.19     -0.12     -0.45      0.19    940.69      1.00\n",
-      " coefs[18]     -0.54      0.66     -0.43     -1.56      0.40   5805.63      1.00\n",
-      " coefs[19]     -0.45      0.68     -0.35     -1.59      0.55   5277.45      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   4861.90      1.00\n",
-      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5058.03      1.00\n",
-      " coefs[22]      0.10      0.05      0.10      0.02      0.19    791.84      1.00\n",
-      " coefs[23]      0.10      0.25      0.10     -0.30      0.52    650.30      1.00\n",
-      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    644.67      1.00\n",
-      " coefs[25]     -0.01      0.24     -0.00     -0.39      0.38    630.09      1.00\n",
-      " coefs[26]      0.11      0.18      0.12     -0.17      0.43    635.35      1.00\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.63      0.14   4712.25      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.60      1.67  10040.11      1.00\n",
-      " coefs[29]      0.05      0.08      0.05     -0.07      0.18    679.39      1.00\n",
-      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    786.03      1.00\n",
-      " coefs[31]     -0.75      0.58     -0.63     -1.63      0.06   5149.75      1.00\n",
-      " coefs[32]      0.09      0.09      0.09     -0.06      0.24    650.45      1.00\n",
-      " coefs[33]      0.13      0.14      0.13     -0.07      0.37    630.38      1.00\n",
-      " coefs[34]      0.14      0.06      0.13      0.03      0.24   1370.58      1.00\n",
-      " coefs[35]      0.35      0.25      0.36     -0.04      0.78    620.21      1.00\n",
-      " coefs[36]      0.36      0.32      0.36     -0.16      0.89    619.37      1.00\n",
-      " coefs[37]      0.19      0.20      0.19     -0.15      0.51    624.44      1.00\n",
-      " coefs[38]     -0.04      0.05     -0.03     -0.11      0.04   1296.38      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    734.11      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    758.44      1.00\n",
-      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   5148.08      1.00\n",
-      " coefs[42]      0.12      0.43      0.13     -0.57      0.81    620.28      1.00\n",
-      " coefs[43]      0.03      0.24      0.03     -0.36      0.41    626.67      1.00\n",
-      " coefs[44]      0.15      0.22      0.16     -0.20      0.52    626.95      1.00\n",
-      " coefs[45]      0.10      0.31      0.11     -0.38      0.61    624.04      1.00\n",
-      " coefs[46]      0.22      0.29      0.23     -0.24      0.70    618.56      1.00\n",
-      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    994.64      1.00\n",
-      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.01    668.23      1.00\n",
-      " coefs[49]     -0.79      0.59     -0.68     -1.64      0.00   4915.15      1.00\n",
-      " coefs[50]     -0.84      0.59     -0.71     -1.69     -0.05   4731.62      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.20    629.43      1.00\n",
-      " coefs[52]     -0.05      0.16     -0.04     -0.31      0.22    625.15      1.00\n",
-      " coefs[53]     -0.14      0.13     -0.13     -0.35      0.08    645.94      1.00\n",
-      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.42   3867.53      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 13 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.06      0.06      2.06      1.96      2.16  10107.97      1.00\n",
-      "  coefs[1]     -0.07      0.04     -0.07     -0.12     -0.01  12223.43      1.00\n",
-      "  coefs[2]     -0.21      0.07     -0.21     -0.33     -0.08   3247.79      1.00\n",
-      "  coefs[3]     -0.34      0.03     -0.34     -0.40     -0.28   7744.39      1.00\n",
-      "  coefs[4]     -0.11      0.04     -0.11     -0.17     -0.05   8886.81      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  10594.79      1.00\n",
-      "  coefs[6]     -0.08      0.30     -0.08     -0.56      0.41   2710.82      1.00\n",
-      "  coefs[7]     -0.52      0.18     -0.52     -0.82     -0.23   2838.19      1.00\n",
-      "  coefs[8]      0.17      0.35      0.17     -0.39      0.74   2697.80      1.00\n",
-      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.02  11093.40      1.00\n",
-      " coefs[10]      0.41      0.65      0.41     -0.67      1.48   3051.80      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.04     -0.52      0.43   3043.81      1.00\n",
-      " coefs[12]      0.06      0.65      0.06     -1.06      1.08   3055.42      1.00\n",
-      " coefs[13]     -0.91      0.65     -0.86     -1.95      0.15   4747.74      1.00\n",
-      " coefs[14]     -0.48      0.66     -0.37     -1.53      0.49   5540.97      1.00\n",
-      " coefs[15]     -0.77      0.56     -0.67     -1.63      0.05   4870.06      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.58     -1.59      0.14   4957.56      1.00\n",
-      " coefs[17]     -0.06      0.18     -0.05     -0.34      0.23    543.36      1.01\n",
-      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.40   5806.90      1.00\n",
-      " coefs[19]     -0.49      0.67     -0.39     -1.56      0.58   5841.70      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5195.52      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.05      0.06   1082.76      1.00\n",
-      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    592.12      1.01\n",
-      " coefs[23]     -0.10      0.26     -0.10     -0.52      0.32    461.09      1.01\n",
-      " coefs[24]      0.00      0.16      0.00     -0.26      0.26    453.93      1.01\n",
-      " coefs[25]     -0.07      0.23     -0.07     -0.44      0.32    426.89      1.01\n",
-      " coefs[26]      0.06      0.18      0.06     -0.25      0.35    434.65      1.01\n",
-      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.14   5038.79      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.69      1.60  11808.60      1.00\n",
-      " coefs[29]      0.04      0.08      0.04     -0.10      0.16    486.47      1.01\n",
-      " coefs[30]     -0.09      0.13     -0.08     -0.31      0.10   1023.19      1.01\n",
-      " coefs[31]      0.02      0.08      0.02     -0.11      0.15    677.56      1.01\n",
-      " coefs[32]      0.07      0.09      0.08     -0.07      0.22    442.33      1.01\n",
-      " coefs[33]      0.13      0.13      0.14     -0.08      0.35    431.07      1.01\n",
-      " coefs[34]      0.91      0.60      0.79      0.11      1.80   5008.02      1.00\n",
-      " coefs[35]      0.31      0.25      0.31     -0.09      0.70    419.67      1.01\n",
-      " coefs[36]      0.32      0.31      0.32     -0.21      0.81    421.90      1.01\n",
-      " coefs[37]      0.18      0.20      0.18     -0.15      0.49    426.28      1.01\n",
-      " coefs[38]     -0.06      0.05     -0.05     -0.13      0.02   1113.26      1.00\n",
-      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    480.00      1.01\n",
-      " coefs[40]      0.10      0.05      0.10      0.02      0.19    500.83      1.01\n",
-      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1035.85      1.01\n",
-      " coefs[42]     -0.00      0.42      0.00     -0.70      0.67    423.22      1.01\n",
-      " coefs[43]     -0.02      0.23     -0.02     -0.40      0.36    427.20      1.01\n",
-      " coefs[44]      0.18      0.22      0.18     -0.17      0.53    421.49      1.01\n",
-      " coefs[45]      0.07      0.30      0.07     -0.42      0.56    416.39      1.01\n",
-      " coefs[46]      0.22      0.28      0.22     -0.25      0.66    423.39      1.01\n",
-      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.06    637.28      1.01\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    457.03      1.01\n",
-      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.00   4772.50      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.75     -1.69     -0.07   4318.31      1.00\n",
-      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.13    423.95      1.01\n",
-      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.13    434.85      1.01\n",
-      " coefs[53]     -0.20      0.13     -0.19     -0.40      0.02    437.62      1.01\n",
-      " coefs[54]     -1.71      0.19     -1.69     -2.01     -1.41   4099.94      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 14 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.97      0.06      1.97      1.87      2.08   9005.66      1.00\n",
-      "  coefs[1]     -0.02      0.03     -0.02     -0.07      0.04  11557.78      1.00\n",
-      "  coefs[2]     -0.06      0.07     -0.06     -0.16      0.05   4138.63      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7839.59      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8500.08      1.00\n",
-      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  10663.93      1.00\n",
-      "  coefs[6]      0.14      0.25      0.13     -0.25      0.55   3159.51      1.00\n",
-      "  coefs[7]     -0.61      0.15     -0.60     -0.85     -0.36   3309.15      1.00\n",
-      "  coefs[8]      0.47      0.29      0.46     -0.03      0.91   3123.20      1.00\n",
-      "  coefs[9]      0.01      0.03      0.01     -0.04      0.05  11937.39      1.00\n",
-      " coefs[10]      0.43      0.65      0.42     -0.71      1.44   3091.25      1.00\n",
-      " coefs[11]     -0.05      0.29     -0.06     -0.57      0.39   3085.88      1.00\n",
-      " coefs[12]      0.07      0.65      0.06     -1.03      1.11   3094.82      1.00\n",
-      " coefs[13]     -1.02      0.63     -0.96     -2.08     -0.04   5050.19      1.00\n",
-      " coefs[14]     -0.47      0.68     -0.36     -1.53      0.53   5346.83      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.64      0.05   4722.58      1.00\n",
-      " coefs[16]     -0.73      0.59     -0.62     -1.62      0.11   4855.77      1.00\n",
-      " coefs[17]     -0.03      0.18     -0.03     -0.31      0.27    720.50      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.43   6038.97      1.00\n",
-      " coefs[19]     -0.47      0.69     -0.38     -1.51      0.66   5416.81      1.00\n",
-      " coefs[20]      0.02      0.98      0.01     -1.59      1.63  13208.44      1.00\n",
-      " coefs[21]      0.02      0.99      0.02     -1.54      1.70  10823.00      1.00\n",
-      " coefs[22]     -0.02      0.07     -0.01     -0.13      0.10   1087.05      1.00\n",
-      " coefs[23]      0.05      0.25      0.05     -0.36      0.48    562.53      1.00\n",
-      " coefs[24]     -0.06      0.17     -0.06     -0.34      0.21    601.03      1.00\n",
-      " coefs[25]     -0.06      0.24     -0.05     -0.46      0.34    550.41      1.00\n",
-      " coefs[26]      0.07      0.19      0.07     -0.23      0.38    546.27      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.15   4953.64      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.57      1.67  10744.99      1.00\n",
-      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    590.76      1.00\n",
-      " coefs[30]      0.02      0.10      0.03     -0.14      0.18    710.84      1.00\n",
-      " coefs[31]     -0.78      0.58     -0.66     -1.62      0.05   5056.04      1.00\n",
-      " coefs[32]      0.04      0.09      0.04     -0.11      0.20    568.43      1.00\n",
-      " coefs[33]      0.15      0.14      0.15     -0.06      0.39    546.49      1.00\n",
-      " coefs[34]      0.91      0.59      0.79      0.11      1.78   4921.83      1.00\n",
-      " coefs[35]      0.35      0.25      0.36     -0.08      0.74    542.19      1.00\n",
-      " coefs[36]      0.33      0.32      0.33     -0.19      0.88    538.22      1.00\n",
-      " coefs[37]      0.13      0.20      0.13     -0.19      0.48    539.85      1.00\n",
-      " coefs[38]      0.02      0.04      0.02     -0.05      0.10   1055.60      1.00\n",
-      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    606.11      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    634.23      1.00\n",
-      " coefs[41]      0.02      0.06      0.03     -0.07      0.12    852.14      1.00\n",
-      " coefs[42]      0.07      0.43      0.08     -0.65      0.77    540.64      1.00\n",
-      " coefs[43]     -0.04      0.24     -0.04     -0.44      0.35    546.56      1.00\n",
-      " coefs[44]      0.16      0.22      0.16     -0.19      0.53    536.30      1.00\n",
-      " coefs[45]      0.11      0.31      0.11     -0.39      0.64    535.15      1.00\n",
-      " coefs[46]      0.18      0.29      0.18     -0.30      0.65    540.24      1.00\n",
-      " coefs[47]     -0.02      0.06     -0.01     -0.12      0.09    669.38      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.03    578.06      1.00\n",
-      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.02   4966.31      1.00\n",
-      " coefs[50]     -0.84      0.58     -0.71     -1.69     -0.06   5157.37      1.00\n",
-      " coefs[51]     -0.05      0.18     -0.04     -0.34      0.24    549.11      1.00\n",
-      " coefs[52]     -0.13      0.17     -0.13     -0.41      0.13    546.42      1.00\n",
-      " coefs[53]     -0.16      0.13     -0.16     -0.39      0.05    554.62      1.00\n",
-      " coefs[54]     -1.64      0.19     -1.63     -1.95     -1.34   4052.25      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 15 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.05      0.06      2.05      1.94      2.14   9177.00      1.00\n",
-      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.00  11743.81      1.00\n",
-      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.02   3628.73      1.00\n",
-      "  coefs[3]     -0.32      0.03     -0.32     -0.38     -0.27   7842.18      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8649.39      1.00\n",
-      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  10859.96      1.00\n",
-      "  coefs[6]      0.37      0.27      0.36     -0.08      0.79   2752.83      1.00\n",
-      "  coefs[7]     -0.83      0.16     -0.83     -1.09     -0.56   2920.83      1.00\n",
-      "  coefs[8]      0.83      0.31      0.82      0.31      1.33   2750.68      1.00\n",
-      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11841.94      1.00\n",
-      " coefs[10]      0.40      0.65      0.39     -0.70      1.44   3135.56      1.00\n",
-      " coefs[11]     -0.01      0.29     -0.02     -0.49      0.47   3135.50      1.00\n",
-      " coefs[12]      0.15      0.65      0.14     -0.89      1.24   3127.87      1.00\n",
-      " coefs[13]     -1.07      0.61     -1.01     -2.06     -0.10   5383.26      1.00\n",
-      " coefs[14]     -0.45      0.66     -0.34     -1.47      0.56   5506.65      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.68     -1.68      0.01   4585.23      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.60     -1.59      0.12   5284.94      1.00\n",
-      " coefs[17]     -0.27      0.22     -0.26     -0.63      0.09   1153.36      1.00\n",
-      " coefs[18]     -0.52      0.67     -0.41     -1.54      0.47   5888.75      1.00\n",
-      " coefs[19]     -0.45      0.68     -0.36     -1.55      0.63   6200.15      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   4811.83      1.00\n",
-      " coefs[21]     -0.78      0.59     -0.67     -1.64      0.01   4300.73      1.00\n",
-      " coefs[22]      0.06      0.06      0.06     -0.04      0.15    790.42      1.01\n",
-      " coefs[23]      0.22      0.24      0.21     -0.16      0.62    521.03      1.01\n",
-      " coefs[24]     -0.03      0.16     -0.03     -0.28      0.23    561.51      1.01\n",
-      " coefs[25]     -0.05      0.23     -0.05     -0.42      0.32    512.26      1.01\n",
-      " coefs[26]      0.00      0.18      0.00     -0.28      0.29    515.81      1.01\n",
-      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.13   5153.89      1.00\n",
-      " coefs[28]      0.02      1.00      0.02     -1.60      1.67  11091.19      1.00\n",
-      " coefs[29]      0.01      0.08      0.01     -0.12      0.14    604.99      1.01\n",
-      " coefs[30]     -0.09      0.13     -0.08     -0.29      0.12   1242.60      1.00\n",
-      " coefs[31]      0.04      0.07      0.04     -0.09      0.15    737.77      1.01\n",
-      " coefs[32]      0.05      0.09      0.05     -0.09      0.19    527.77      1.01\n",
-      " coefs[33]      0.14      0.13      0.14     -0.06      0.35    518.80      1.01\n",
-      " coefs[34]      0.92      0.59      0.80      0.10      1.76   4699.77      1.00\n",
-      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    503.71      1.01\n",
-      " coefs[36]      0.31      0.31      0.31     -0.20      0.79    506.01      1.01\n",
-      " coefs[37]      0.10      0.19      0.10     -0.22      0.41    509.89      1.01\n",
-      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    903.45      1.01\n",
-      " coefs[39]      0.05      0.07      0.05     -0.06      0.17    542.48      1.01\n",
-      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    655.54      1.01\n",
-      " coefs[41]      0.02      0.05      0.02     -0.07      0.10    905.27      1.01\n",
-      " coefs[42]      0.04      0.41      0.04     -0.61      0.71    503.61      1.01\n",
-      " coefs[43]     -0.00      0.23     -0.00     -0.37      0.37    512.92      1.01\n",
-      " coefs[44]      0.16      0.21      0.15     -0.17      0.51    504.57      1.01\n",
-      " coefs[45]      0.07      0.29      0.07     -0.40      0.55    502.69      1.01\n",
-      " coefs[46]      0.18      0.27      0.18     -0.25      0.64    506.09      1.01\n",
-      " coefs[47]     -0.07      0.07     -0.07     -0.18      0.04    782.66      1.01\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    544.83      1.01\n",
-      " coefs[49]     -0.79      0.60     -0.67     -1.63      0.02   4838.35      1.00\n",
-      " coefs[50]     -0.87      0.58     -0.75     -1.69     -0.08   4164.47      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.36      0.18    515.73      1.01\n",
-      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.13    507.39      1.01\n",
-      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.01    515.72      1.01\n",
-      " coefs[54]     -1.66      0.18     -1.64     -1.96     -1.36   4343.76      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 16 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9179.36      1.00\n",
-      "  coefs[1]      0.01      0.03      0.01     -0.05      0.07  10791.72      1.00\n",
-      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3510.14      1.00\n",
-      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   7615.67      1.00\n",
-      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8998.44      1.00\n",
-      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10867.82      1.00\n",
-      "  coefs[6]      0.50      0.29      0.49      0.02      0.99   2920.24      1.00\n",
-      "  coefs[7]     -0.79      0.18     -0.79     -1.08     -0.48   3039.41      1.00\n",
-      "  coefs[8]      0.87      0.35      0.86      0.27      1.42   2922.72      1.00\n",
-      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11173.31      1.00\n",
-      " coefs[10]      0.46      0.65      0.45     -0.57      1.54   3308.73      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.43   3324.22      1.00\n",
-      " coefs[12]      0.08      0.65      0.08     -0.96      1.14   3310.11      1.00\n",
-      " coefs[13]     -1.05      0.62     -0.99     -2.00     -0.03   4531.52      1.00\n",
-      " coefs[14]     -0.47      0.67     -0.36     -1.51      0.52   5577.25      1.00\n",
-      " coefs[15]     -0.78      0.58     -0.68     -1.64      0.08   4391.98      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.60     -1.57      0.15   4813.23      1.00\n",
-      " coefs[17]     -0.29      0.22     -0.28     -0.65      0.08   1050.49      1.00\n",
-      " coefs[18]     -0.55      0.67     -0.43     -1.57      0.42   5579.16      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.60      0.54   5415.16      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5013.34      1.00\n",
-      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.03   4630.94      1.00\n",
-      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    831.29      1.00\n",
-      " coefs[23]      0.12      0.24      0.12     -0.28      0.51    565.03      1.01\n",
-      " coefs[24]      0.10      0.15      0.11     -0.14      0.36    566.50      1.01\n",
-      " coefs[25]     -0.06      0.23     -0.06     -0.44      0.31    544.78      1.01\n",
-      " coefs[26]      0.04      0.18      0.04     -0.25      0.33    556.89      1.01\n",
-      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   4905.08      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.59      1.69  10411.65      1.00\n",
-      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    596.47      1.01\n",
-      " coefs[30]      0.04      0.09      0.04     -0.11      0.18    684.25      1.00\n",
-      " coefs[31]      0.04      0.07      0.04     -0.07      0.15    717.08      1.01\n",
-      " coefs[32]      0.09      0.09      0.10     -0.06      0.23    560.88      1.01\n",
-      " coefs[33]      0.15      0.13      0.15     -0.06      0.36    550.32      1.01\n",
-      " coefs[34]      0.90      0.60      0.79      0.09      1.79   4522.53      1.00\n",
-      " coefs[35]      0.33      0.24      0.33     -0.06      0.72    542.54      1.01\n",
-      " coefs[36]      0.31      0.31      0.31     -0.19      0.81    538.21      1.01\n",
-      " coefs[37]      0.17      0.19      0.18     -0.16      0.47    545.27      1.01\n",
-      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    873.71      1.00\n",
-      " coefs[39]      0.02      0.08      0.02     -0.11      0.15    679.04      1.00\n",
-      " coefs[40]      0.02      0.05      0.02     -0.05      0.10    628.08      1.01\n",
-      " coefs[41]     -0.80      0.59     -0.67     -1.67      0.03   4771.75      1.00\n",
-      " coefs[42]      0.02      0.41      0.03     -0.65      0.68    537.69      1.01\n",
-      " coefs[43]     -0.02      0.23     -0.02     -0.38      0.36    545.99      1.01\n",
-      " coefs[44]      0.19      0.21      0.19     -0.18      0.51    539.59      1.01\n",
-      " coefs[45]      0.07      0.30      0.07     -0.41      0.55    540.83      1.01\n",
-      " coefs[46]      0.22      0.28      0.23     -0.23      0.66    538.97      1.01\n",
-      " coefs[47]     -0.02      0.07     -0.02     -0.13      0.09    789.16      1.00\n",
-      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.04    598.54      1.01\n",
-      " coefs[49]     -0.79      0.60     -0.67     -1.65      0.02   4719.61      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.72     -1.70     -0.07   4374.23      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    547.36      1.01\n",
-      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.16    550.52      1.01\n",
-      " coefs[53]     -0.12      0.13     -0.12     -0.33      0.08    546.83      1.01\n",
-      " coefs[54]     -1.68      0.18     -1.67     -1.98     -1.38   3683.28      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 17 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.02      0.06      2.02      1.92      2.12   9825.76      1.00\n",
-      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.01  11491.29      1.00\n",
-      "  coefs[2]     -0.12      0.07     -0.12     -0.24     -0.02   4035.17      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7508.58      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8850.54      1.00\n",
-      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  10832.36      1.00\n",
-      "  coefs[6]     -0.03      0.25     -0.03     -0.43      0.39   3103.03      1.00\n",
-      "  coefs[7]     -0.49      0.15     -0.49     -0.74     -0.24   3302.29      1.00\n",
-      "  coefs[8]      0.26      0.29      0.26     -0.20      0.74   3075.37      1.00\n",
-      "  coefs[9]     -0.08      0.03     -0.08     -0.12     -0.03  11096.54      1.00\n",
-      " coefs[10]      0.47      0.64      0.47     -0.61      1.49   3268.81      1.00\n",
-      " coefs[11]     -0.08      0.29     -0.08     -0.59      0.35   3299.38      1.00\n",
-      " coefs[12]      0.07      0.64      0.06     -1.04      1.07   3296.69      1.00\n",
-      " coefs[13]     -1.04      0.62     -0.98     -2.07     -0.09   4800.78      1.00\n",
-      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.52   5846.17      1.00\n",
-      " coefs[15]     -0.79      0.57     -0.69     -1.62      0.06   4206.97      1.00\n",
-      " coefs[16]     -0.71      0.58     -0.60     -1.58      0.14   5088.30      1.00\n",
-      " coefs[17]     -0.05      0.18     -0.05     -0.33      0.24    599.68      1.01\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.45   5927.75      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.58   5998.88      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.67     -1.62      0.01   4825.52      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1133.37      1.00\n",
-      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    589.43      1.01\n",
-      " coefs[23]      0.15      0.25      0.15     -0.26      0.56    468.13      1.01\n",
-      " coefs[24]      0.13      0.16      0.13     -0.14      0.37    471.51      1.01\n",
-      " coefs[25]     -0.03      0.23     -0.03     -0.41      0.36    459.24      1.01\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    473.85      1.01\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.62      0.14   4955.11      1.00\n",
-      " coefs[28]      0.01      0.99      0.01     -1.53      1.73  10769.97      1.00\n",
-      " coefs[29]     -0.00      0.08     -0.01     -0.13      0.13    522.04      1.01\n",
-      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    527.10      1.01\n",
-      " coefs[31]      0.04      0.07      0.04     -0.08      0.16    648.90      1.01\n",
-      " coefs[32]      0.10      0.09      0.10     -0.04      0.25    479.99      1.01\n",
-      " coefs[33]      0.12      0.13      0.12     -0.10      0.34    472.55      1.01\n",
-      " coefs[34]      0.11      0.05      0.11      0.03      0.20    757.54      1.01\n",
-      " coefs[35]      0.29      0.25      0.29     -0.10      0.70    452.91      1.01\n",
-      " coefs[36]      0.34      0.31      0.34     -0.21      0.83    453.74      1.01\n",
-      " coefs[37]      0.16      0.20      0.16     -0.17      0.48    458.11      1.01\n",
-      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    759.34      1.01\n",
-      " coefs[39]     -0.03      0.08     -0.03     -0.17      0.10    622.87      1.01\n",
-      " coefs[40]      0.08      0.05      0.08     -0.00      0.17    627.81      1.01\n",
-      " coefs[41]     -0.78      0.60     -0.66     -1.68      0.02   5038.60      1.00\n",
-      " coefs[42]     -0.02      0.42     -0.02     -0.68      0.70    454.27      1.01\n",
-      " coefs[43]     -0.05      0.23     -0.05     -0.44      0.33    462.64      1.01\n",
-      " coefs[44]      0.19      0.22      0.18     -0.17      0.54    455.92      1.01\n",
-      " coefs[45]      0.11      0.30      0.11     -0.40      0.59    455.52      1.01\n",
-      " coefs[46]      0.20      0.28      0.20     -0.28      0.64    452.79      1.01\n",
-      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    647.18      1.01\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.02    503.96      1.01\n",
-      " coefs[49]     -0.81      0.59     -0.69     -1.66     -0.01   4790.18      1.00\n",
-      " coefs[50]     -0.85      0.59     -0.73     -1.69     -0.06   4353.25      1.00\n",
-      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.16    465.74      1.01\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.39      0.14    460.95      1.01\n",
-      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    466.41      1.01\n",
-      " coefs[54]     -1.69      0.18     -1.67     -1.97     -1.38   4247.42      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 18 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.01      0.06      2.01      1.91      2.11   9222.07      1.00\n",
-      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.02  11037.73      1.00\n",
-      "  coefs[2]     -0.11      0.06     -0.11     -0.22     -0.01   3896.77      1.00\n",
-      "  coefs[3]     -0.38      0.03     -0.38     -0.44     -0.33   7697.55      1.00\n",
-      "  coefs[4]     -0.04      0.03     -0.05     -0.10      0.01   8703.86      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10405.15      1.00\n",
-      "  coefs[6]      0.12      0.23      0.12     -0.24      0.51   2968.23      1.00\n",
-      "  coefs[7]     -0.60      0.14     -0.60     -0.83     -0.36   3184.79      1.00\n",
-      "  coefs[8]      0.42      0.27      0.42     -0.02      0.86   2967.49      1.00\n",
-      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  11147.01      1.00\n",
-      " coefs[10]      0.44      0.65      0.44     -0.67      1.48   2962.23      1.00\n",
-      " coefs[11]     -0.08      0.29     -0.08     -0.56      0.40   2974.48      1.00\n",
-      " coefs[12]      0.07      0.65      0.07     -1.00      1.15   2969.88      1.00\n",
-      " coefs[13]     -0.99      0.64     -0.93     -2.05      0.01   4667.16      1.00\n",
-      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.52   5983.57      1.00\n",
-      " coefs[15]     -0.78      0.58     -0.67     -1.66      0.06   4759.51      1.00\n",
-      " coefs[16]     -0.70      0.58     -0.60     -1.57      0.13   5111.37      1.00\n",
-      " coefs[17]     -0.02      0.17     -0.02     -0.30      0.25    723.30      1.01\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   5519.08      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.38     -1.58      0.55   5869.82      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.67     -1.63      0.01   4721.83      1.00\n",
-      " coefs[21]     -0.77      0.58     -0.66     -1.60      0.03   5203.05      1.00\n",
-      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    742.09      1.01\n",
-      " coefs[23]      0.05      0.25      0.05     -0.36      0.45    635.21      1.01\n",
-      " coefs[24]     -0.03      0.16     -0.03     -0.30      0.22    658.36      1.01\n",
-      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.30    612.30      1.01\n",
-      " coefs[26]      0.04      0.18      0.05     -0.26      0.33    624.90      1.01\n",
-      " coefs[27]     -0.70      0.62     -0.58     -1.60      0.17   5010.88      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.62      1.66  10001.87      1.00\n",
-      " coefs[29]      0.03      0.08      0.03     -0.11      0.15    670.66      1.01\n",
-      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    741.75      1.01\n",
-      " coefs[31]     -0.00      0.08     -0.00     -0.13      0.12    871.75      1.01\n",
-      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    641.81      1.01\n",
-      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    606.63      1.01\n",
-      " coefs[34]      0.15      0.06      0.14      0.05      0.25   1321.74      1.00\n",
-      " coefs[35]      0.33      0.24      0.33     -0.08      0.71    602.00      1.01\n",
-      " coefs[36]      0.33      0.31      0.33     -0.17      0.84    599.72      1.01\n",
-      " coefs[37]      0.18      0.20      0.18     -0.14      0.50    607.37      1.01\n",
-      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    825.58      1.01\n",
-      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    688.22      1.01\n",
-      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    737.72      1.01\n",
-      " coefs[41]      0.01      0.07      0.02     -0.10      0.12   1492.59      1.00\n",
-      " coefs[42]      0.02      0.41      0.02     -0.68      0.69    602.54      1.01\n",
-      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.34    613.82      1.01\n",
-      " coefs[44]      0.19      0.21      0.19     -0.16      0.54    604.50      1.01\n",
-      " coefs[45]      0.13      0.30      0.14     -0.39      0.59    603.75      1.01\n",
-      " coefs[46]      0.23      0.28      0.23     -0.23      0.68    609.11      1.01\n",
-      " coefs[47]     -0.07      0.07     -0.06     -0.18      0.05    933.07      1.00\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    672.42      1.01\n",
-      " coefs[49]     -0.80      0.59     -0.69     -1.65      0.00   4630.65      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4276.88      1.00\n",
-      " coefs[51]     -0.07      0.17     -0.07     -0.35      0.21    624.71      1.01\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.12    615.24      1.01\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    608.75      1.01\n",
-      " coefs[54]     -1.65      0.19     -1.64     -1.94     -1.35   3844.77      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 19 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.09      0.06      2.09      1.99      2.20   9900.43      1.00\n",
-      "  coefs[1]     -0.09      0.04     -0.09     -0.15     -0.03  12225.38      1.00\n",
-      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3777.37      1.00\n",
-      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   8256.62      1.00\n",
-      "  coefs[4]     -0.13      0.04     -0.13     -0.18     -0.07   9095.25      1.00\n",
-      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  11139.58      1.00\n",
-      "  coefs[6]      0.43      0.28      0.42     -0.03      0.90   3032.91      1.00\n",
-      "  coefs[7]     -0.85      0.17     -0.84     -1.13     -0.56   3189.63      1.00\n",
-      "  coefs[8]      0.87      0.33      0.86      0.30      1.40   3022.08      1.00\n",
-      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  12442.31      1.00\n",
-      " coefs[10]      0.41      0.65      0.40     -0.72      1.41   3331.08      1.00\n",
-      " coefs[11]     -0.06      0.29     -0.07     -0.54      0.41   3341.18      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -1.03      1.10   3333.96      1.00\n",
-      " coefs[13]     -1.07      0.61     -1.01     -2.05     -0.08   5218.74      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.54      0.52   5822.97      1.00\n",
-      " coefs[15]     -0.79      0.57     -0.68     -1.65      0.06   4591.28      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.61     -1.62      0.14   5379.81      1.00\n",
-      " coefs[17]      0.00      0.17      0.01     -0.26      0.29    769.45      1.00\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   6037.22      1.00\n",
-      " coefs[19]     -0.44      0.68     -0.36     -1.52      0.62   6056.28      1.00\n",
-      " coefs[20]     -0.77      0.60     -0.65     -1.63      0.03   4989.46      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1593.75      1.00\n",
-      " coefs[22]      0.09      0.05      0.10      0.01      0.18    737.03      1.00\n",
-      " coefs[23]      0.20      0.25      0.21     -0.21      0.61    633.08      1.00\n",
-      " coefs[24]      0.08      0.16      0.09     -0.17      0.34    632.23      1.00\n",
-      " coefs[25]     -0.10      0.24     -0.10     -0.46      0.31    630.33      1.00\n",
-      " coefs[26]      0.08      0.18      0.08     -0.21      0.39    615.33      1.00\n",
-      " coefs[27]     -0.67      0.63     -0.55     -1.59      0.22   5405.23      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.67      1.63  11841.95      1.00\n",
-      " coefs[29]      0.01      0.08      0.01     -0.13      0.13    726.36      1.00\n",
-      " coefs[30]      0.10      0.09      0.10     -0.05      0.23    715.32      1.00\n",
-      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1298.58      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    653.45      1.00\n",
-      " coefs[33]      0.11      0.13      0.11     -0.12      0.32    620.44      1.00\n",
-      " coefs[34]      0.93      0.59      0.82      0.12      1.77   4759.24      1.00\n",
-      " coefs[35]      0.35      0.25      0.36     -0.04      0.76    611.41      1.00\n",
-      " coefs[36]      0.34      0.31      0.35     -0.18      0.84    609.07      1.00\n",
-      " coefs[37]      0.18      0.20      0.18     -0.16      0.49    617.89      1.00\n",
-      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    798.81      1.00\n",
-      " coefs[39]     -0.05      0.09     -0.05     -0.20      0.09    945.47      1.00\n",
-      " coefs[40]      0.08      0.05      0.08     -0.00      0.16    775.94      1.00\n",
-      " coefs[41]     -0.79      0.59     -0.67     -1.68      0.02   5087.86      1.00\n",
-      " coefs[42]      0.02      0.42      0.03     -0.65      0.71    610.24      1.00\n",
-      " coefs[43]      0.01      0.23      0.01     -0.36      0.40    613.65      1.00\n",
-      " coefs[44]      0.16      0.22      0.16     -0.19      0.52    615.17      1.00\n",
-      " coefs[45]      0.04      0.30      0.05     -0.46      0.52    611.35      1.00\n",
-      " coefs[46]      0.18      0.28      0.19     -0.27      0.65    618.14      1.00\n",
-      " coefs[47]     -0.86      0.56     -0.74     -1.70     -0.08   4596.20      1.00\n",
-      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    670.20      1.00\n",
-      " coefs[49]      0.03      1.00      0.04     -1.57      1.71  11583.95      1.00\n",
-      " coefs[50]     -0.87      0.57     -0.76     -1.69     -0.08   4887.46      1.00\n",
-      " coefs[51]     -0.14      0.17     -0.14     -0.41      0.14    618.30      1.00\n",
-      " coefs[52]     -0.19      0.16     -0.19     -0.45      0.08    619.52      1.00\n",
-      " coefs[53]     -0.19      0.13     -0.18     -0.40      0.02    624.71      1.00\n",
-      " coefs[54]     -1.69      0.19     -1.68     -1.99     -1.39   4128.48      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 20 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.89      0.06      1.89      1.79      1.99   9246.42      1.00\n",
-      "  coefs[1]     -0.08      0.03     -0.08     -0.13     -0.02  11208.54      1.00\n",
-      "  coefs[2]      0.01      0.06      0.01     -0.09      0.11   3502.44      1.00\n",
-      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7328.68      1.00\n",
-      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   7942.68      1.00\n",
-      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11139.29      1.00\n",
-      "  coefs[6]      0.47      0.24      0.45      0.07      0.84   2645.70      1.00\n",
-      "  coefs[7]     -0.73      0.15     -0.73     -0.97     -0.49   2807.38      1.00\n",
-      "  coefs[8]      0.85      0.28      0.83      0.40      1.30   2626.09      1.00\n",
-      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.01  12620.86      1.00\n",
-      " coefs[10]      0.39      0.65      0.38     -0.73      1.44   2934.75      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.04     -0.51      0.45   2942.71      1.00\n",
-      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2939.57      1.00\n",
-      " coefs[13]     -0.97      0.64     -0.91     -1.94      0.13   4606.51      1.00\n",
-      " coefs[14]     -0.46      0.66     -0.35     -1.52      0.51   5983.50      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.07   3909.10      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.61     -1.62      0.11   5133.14      1.00\n",
-      " coefs[17]     -0.27      0.23     -0.26     -0.65      0.09    826.22      1.00\n",
-      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5573.30      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.38     -1.56      0.56   5610.96      1.00\n",
-      " coefs[20]      0.02      0.97      0.02     -1.57      1.63  10854.73      1.00\n",
-      " coefs[21]      0.01      0.03      0.01     -0.04      0.06    980.00      1.00\n",
-      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    642.18      1.01\n",
-      " coefs[23]      0.01      0.25      0.01     -0.39      0.44    445.60      1.01\n",
-      " coefs[24]     -0.04      0.16     -0.04     -0.30      0.23    464.65      1.01\n",
-      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.32    422.35      1.01\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    425.48      1.01\n",
-      " coefs[27]     -0.70      0.61     -0.59     -1.58      0.16   5206.67      1.00\n",
-      " coefs[28]      0.03      0.99      0.04     -1.55      1.70  10690.05      1.00\n",
-      " coefs[29]      0.11      0.08      0.11     -0.02      0.23    447.83      1.01\n",
-      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    609.85      1.01\n",
-      " coefs[31]      0.03      0.08      0.03     -0.10      0.15    668.65      1.00\n",
-      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    435.76      1.01\n",
-      " coefs[33]      0.15      0.13      0.15     -0.05      0.39    423.61      1.01\n",
-      " coefs[34]      0.92      0.59      0.80      0.10      1.77   4889.49      1.00\n",
-      " coefs[35]      0.35      0.24      0.35     -0.05      0.76    416.61      1.01\n",
-      " coefs[36]      0.32      0.31      0.32     -0.17      0.87    414.14      1.01\n",
-      " coefs[37]      0.18      0.20      0.18     -0.15      0.50    415.80      1.01\n",
-      " coefs[38]     -0.04      0.05     -0.04     -0.12      0.04    964.69      1.00\n",
-      " coefs[39]     -0.03      0.08     -0.02     -0.17      0.10    572.20      1.01\n",
-      " coefs[40]      0.07      0.05      0.07     -0.02      0.15    548.93      1.01\n",
-      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   4809.95      1.00\n",
-      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    414.43      1.01\n",
-      " coefs[43]      0.00      0.23      0.01     -0.36      0.42    420.25      1.01\n",
-      " coefs[44]      0.18      0.22      0.19     -0.18      0.53    414.59      1.01\n",
-      " coefs[45]      0.13      0.30      0.13     -0.35      0.65    412.93      1.01\n",
-      " coefs[46]      0.22      0.28      0.22     -0.25      0.68    414.62      1.01\n",
-      " coefs[47]     -0.12      0.09     -0.12     -0.27      0.01    846.25      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.02    450.84      1.01\n",
-      " coefs[49]     -0.80      0.59     -0.69     -1.64     -0.00   5076.40      1.00\n",
-      " coefs[50]     -0.83      0.58     -0.70     -1.66     -0.04   4703.44      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.19    420.59      1.01\n",
-      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    421.82      1.01\n",
-      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    430.31      1.01\n",
-      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   3704.67      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 21 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9762.19      1.00\n",
-      "  coefs[1]     -0.15      0.04     -0.15     -0.21     -0.09  11181.90      1.00\n",
-      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3538.15      1.00\n",
-      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.21   7643.43      1.00\n",
-      "  coefs[4]     -0.11      0.03     -0.11     -0.16     -0.05   8365.70      1.00\n",
-      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10974.91      1.00\n",
-      "  coefs[6]      0.16      0.29      0.16     -0.31      0.64   2862.26      1.00\n",
-      "  coefs[7]     -0.60      0.18     -0.60     -0.90     -0.32   2967.20      1.00\n",
-      "  coefs[8]      0.53      0.34      0.52     -0.03      1.09   2843.52      1.00\n",
-      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11309.82      1.00\n",
-      " coefs[10]      0.41      0.65      0.40     -0.67      1.47   3281.18      1.00\n",
-      " coefs[11]      0.01      0.29      0.01     -0.48      0.47   3284.19      1.00\n",
-      " coefs[12]      0.09      0.65      0.09     -0.96      1.18   3281.82      1.00\n",
-      " coefs[13]     -1.04      0.62     -0.98     -2.00     -0.03   4929.61      1.00\n",
-      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.55   6576.05      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.66      0.04   4629.92      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5257.19      1.00\n",
-      " coefs[17]     -0.06      0.17     -0.06     -0.35      0.21    740.58      1.00\n",
-      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.44   5842.99      1.00\n",
-      " coefs[19]     -0.43      0.67     -0.34     -1.50      0.63   5996.43      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.62      0.02   5050.51      1.00\n",
-      " coefs[21]     -0.77      0.60     -0.66     -1.63      0.04   4806.38      1.00\n",
-      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    781.54      1.00\n",
-      " coefs[23]      0.14      0.24      0.14     -0.25      0.54    588.58      1.00\n",
-      " coefs[24]      0.05      0.15      0.05     -0.21      0.30    592.89      1.00\n",
-      " coefs[25]     -0.12      0.23     -0.12     -0.49      0.26    569.03      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.26      0.32    570.36      1.00\n",
-      " coefs[27]     -0.70      0.62     -0.58     -1.59      0.18   5348.57      1.00\n",
-      " coefs[28]      0.03      0.99      0.02     -1.56      1.72  10094.24      1.00\n",
-      " coefs[29]      0.07      0.08      0.07     -0.04      0.21    603.97      1.00\n",
-      " coefs[30]      0.04      0.09      0.04     -0.12      0.19    749.44      1.00\n",
-      " coefs[31]     -0.00      0.08      0.00     -0.13      0.13    924.25      1.00\n",
-      " coefs[32]      0.08      0.09      0.08     -0.07      0.22    588.87      1.00\n",
-      " coefs[33]      0.10      0.13      0.10     -0.11      0.31    568.07      1.00\n",
-      " coefs[34]      0.14      0.06      0.14      0.04      0.24   1356.03      1.00\n",
-      " coefs[35]      0.28      0.24      0.28     -0.09      0.69    556.98      1.00\n",
-      " coefs[36]      0.31      0.31      0.31     -0.18      0.82    553.33      1.00\n",
-      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    559.88      1.00\n",
-      " coefs[38]      0.01      0.03      0.01     -0.04      0.07    757.07      1.00\n",
-      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    647.92      1.00\n",
-      " coefs[40]      0.04      0.05      0.04     -0.04      0.12    641.85      1.00\n",
-      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1297.18      1.00\n",
-      " coefs[42]      0.00      0.41      0.00     -0.64      0.69    553.97      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    559.55      1.00\n",
-      " coefs[44]      0.19      0.21      0.20     -0.15      0.54    560.54      1.00\n",
-      " coefs[45]      0.08      0.29      0.08     -0.39      0.56    556.92      1.00\n",
-      " coefs[46]      0.24      0.28      0.24     -0.18      0.72    555.62      1.00\n",
-      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    894.80      1.00\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    627.40      1.00\n",
-      " coefs[49]      0.04      1.01      0.03     -1.59      1.70  10909.59      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.09   4571.07      1.00\n",
-      " coefs[51]     -0.15      0.17     -0.15     -0.41      0.13    561.78      1.00\n",
-      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.12    562.22      1.00\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.37      0.05    562.71      1.00\n",
-      " coefs[54]     -1.66      0.18     -1.65     -1.96     -1.38   4130.36      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 22 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.04      0.06      2.04      1.94      2.15   8792.94      1.00\n",
-      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11601.13      1.00\n",
-      "  coefs[2]     -0.16      0.07     -0.16     -0.27     -0.05   4312.41      1.00\n",
-      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   6939.66      1.00\n",
-      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.05   7411.87      1.00\n",
-      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  10025.50      1.00\n",
-      "  coefs[6]     -0.04      0.25     -0.04     -0.45      0.37   3331.37      1.00\n",
-      "  coefs[7]     -0.57      0.15     -0.57     -0.82     -0.32   3563.81      1.00\n",
-      "  coefs[8]      0.29      0.29      0.29     -0.18      0.78   3339.59      1.00\n",
-      "  coefs[9]      0.04      0.03      0.04     -0.00      0.09  10370.34      1.00\n",
-      " coefs[10]      0.39      0.66      0.39     -0.69      1.46   3233.84      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.42   3237.79      1.00\n",
-      " coefs[12]      0.11      0.65      0.11     -1.03      1.12   3237.01      1.00\n",
-      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   4483.64      1.00\n",
-      " coefs[14]     -0.47      0.67     -0.36     -1.52      0.52   5759.36      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.04   4528.41      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.60     -1.60      0.14   4801.30      1.00\n",
-      " coefs[17]     -0.07      0.17     -0.07     -0.35      0.22    832.85      1.00\n",
-      " coefs[18]     -0.53      0.66     -0.42     -1.57      0.40   5510.81      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5378.76      1.00\n",
-      " coefs[20]      0.02      0.98      0.02     -1.59      1.66  12635.21      1.00\n",
-      " coefs[21]      0.00      0.03      0.00     -0.05      0.05   1578.97      1.00\n",
-      " coefs[22]      0.07      0.06      0.07     -0.03      0.15    799.11      1.00\n",
-      " coefs[23]      0.08      0.25      0.08     -0.32      0.50    631.44      1.00\n",
-      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    665.12      1.00\n",
-      " coefs[25]     -0.16      0.23     -0.16     -0.52      0.25    629.61      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    649.75      1.00\n",
-      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.12   4951.62      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.63      1.60   9968.12      1.00\n",
-      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    691.13      1.00\n",
-      " coefs[30]      0.04      0.09      0.04     -0.10      0.20    752.47      1.00\n",
-      " coefs[31]      0.01      0.08      0.02     -0.12      0.14   1127.34      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    667.50      1.00\n",
-      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    635.17      1.00\n",
-      " coefs[34]      0.14      0.06      0.14      0.04      0.25   1416.76      1.00\n",
-      " coefs[35]      0.33      0.25      0.33     -0.09      0.72    623.44      1.00\n",
-      " coefs[36]      0.34      0.32      0.34     -0.16      0.87    612.20      1.00\n",
-      " coefs[37]      0.15      0.20      0.15     -0.19      0.46    622.84      1.00\n",
-      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.03   1609.92      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    723.00      1.00\n",
-      " coefs[40]      0.09      0.05      0.09      0.00      0.17    829.79      1.00\n",
-      " coefs[41]      0.03      0.05      0.03     -0.05      0.12    884.95      1.00\n",
-      " coefs[42]      0.05      0.42      0.05     -0.64      0.73    619.81      1.00\n",
-      " coefs[43]     -0.03      0.24     -0.02     -0.43      0.34    621.58      1.00\n",
-      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    617.23      1.00\n",
-      " coefs[45]      0.09      0.30      0.09     -0.39      0.60    618.28      1.00\n",
-      " coefs[46]      0.22      0.28      0.23     -0.23      0.69    608.95      1.00\n",
-      " coefs[47]     -0.02      0.06     -0.02     -0.13      0.08    790.25      1.00\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.21      0.00    689.44      1.00\n",
-      " coefs[49]     -0.81      0.60     -0.70     -1.67      0.00   4347.16      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4436.04      1.00\n",
-      " coefs[51]     -0.14      0.17     -0.13     -0.41      0.15    622.46      1.00\n",
-      " coefs[52]     -0.14      0.16     -0.14     -0.41      0.12    634.06      1.00\n",
-      " coefs[53]     -0.11      0.13     -0.11     -0.32      0.11    641.85      1.00\n",
-      " coefs[54]     -1.65      0.18     -1.63     -1.93     -1.33   3934.98      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 23 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.93      0.06      1.93      1.83      2.03   9689.88      1.00\n",
-      "  coefs[1]     -0.05      0.03     -0.05     -0.10      0.01  12545.20      1.00\n",
-      "  coefs[2]     -0.02      0.07     -0.02     -0.13      0.09   3898.07      1.00\n",
-      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   7686.11      1.00\n",
-      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   8700.67      1.00\n",
-      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13  10401.49      1.00\n",
-      "  coefs[6]      0.26      0.25      0.25     -0.14      0.68   2980.05      1.00\n",
-      "  coefs[7]     -0.67      0.15     -0.67     -0.92     -0.42   3112.42      1.00\n",
-      "  coefs[8]      0.57      0.29      0.56      0.11      1.07   2948.98      1.00\n",
-      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  12414.78      1.00\n",
-      " coefs[10]      0.44      0.65      0.43     -0.63      1.52   2846.10      1.00\n",
-      " coefs[11]     -0.01      0.29     -0.02     -0.51      0.45   2871.59      1.00\n",
-      " coefs[12]      0.10      0.65      0.10     -0.98      1.17   2857.64      1.00\n",
-      " coefs[13]     -1.09      0.63     -1.03     -2.05     -0.01   4990.59      1.00\n",
-      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.54   6165.47      1.00\n",
-      " coefs[15]     -0.81      0.57     -0.71     -1.69      0.02   5048.22      1.00\n",
-      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.08   4824.68      1.00\n",
-      " coefs[17]     -0.16      0.19     -0.15     -0.48      0.13    848.87      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.40   5827.61      1.00\n",
-      " coefs[19]     -0.45      0.67     -0.36     -1.53      0.58   6544.98      1.00\n",
-      " coefs[20]     -0.76      0.59     -0.65     -1.61      0.04   5423.70      1.00\n",
-      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1947.02      1.00\n",
-      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    874.06      1.00\n",
-      " coefs[23]      0.07      0.24      0.07     -0.32      0.47    585.54      1.00\n",
-      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.23    603.12      1.00\n",
-      " coefs[25]     -0.07      0.23     -0.08     -0.44      0.32    562.41      1.00\n",
-      " coefs[26]     -0.00      0.18     -0.00     -0.28      0.31    574.26      1.00\n",
-      " coefs[27]     -0.62      0.64     -0.50     -1.58      0.31   5547.06      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.58      1.68  10670.31      1.00\n",
-      " coefs[29]      0.08      0.08      0.08     -0.04      0.21    627.27      1.00\n",
-      " coefs[30]      0.01      0.09      0.01     -0.15      0.16    741.73      1.00\n",
-      " coefs[31]     -0.00      0.08      0.00     -0.12      0.13    840.86      1.00\n",
-      " coefs[32]      0.07      0.09      0.06     -0.08      0.21    588.23      1.00\n",
-      " coefs[33]      0.17      0.13      0.16     -0.04      0.39    570.20      1.00\n",
-      " coefs[34]      0.92      0.59      0.80      0.10      1.77   5030.01      1.00\n",
-      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    559.22      1.00\n",
-      " coefs[36]      0.30      0.31      0.29     -0.20      0.82    552.54      1.00\n",
-      " coefs[37]      0.15      0.19      0.14     -0.17      0.47    551.24      1.00\n",
-      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05   1035.24      1.00\n",
-      " coefs[39]     -0.00      0.08     -0.00     -0.13      0.12    664.01      1.00\n",
-      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.07    667.57      1.00\n",
-      " coefs[41]     -0.03      0.07     -0.02     -0.13      0.09   1390.68      1.00\n",
-      " coefs[42]      0.02      0.41      0.01     -0.65      0.69    555.94      1.00\n",
-      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.33    561.70      1.00\n",
-      " coefs[44]      0.16      0.21      0.15     -0.18      0.51    561.34      1.00\n",
-      " coefs[45]      0.06      0.30      0.06     -0.43      0.54    558.07      1.00\n",
-      " coefs[46]      0.19      0.28      0.19     -0.27      0.63    558.31      1.00\n",
-      " coefs[47]     -0.10      0.09     -0.10     -0.23      0.05   1359.88      1.00\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    608.20      1.00\n",
-      " coefs[49]      0.03      1.00      0.02     -1.51      1.75  12878.55      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.07   4962.08      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.38      0.16    577.83      1.00\n",
-      " coefs[52]     -0.08      0.16     -0.08     -0.35      0.17    562.72      1.00\n",
-      " coefs[53]     -0.11      0.13     -0.11     -0.31      0.10    564.13      1.00\n",
-      " coefs[54]     -1.61      0.18     -1.60     -1.89     -1.29   4385.25      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 24 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.07      0.06      2.07      1.97      2.18   9888.07      1.00\n",
-      "  coefs[1]     -0.04      0.04     -0.04     -0.10      0.02  10935.57      1.00\n",
-      "  coefs[2]     -0.22      0.07     -0.22     -0.34     -0.10   3416.86      1.00\n",
-      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   8028.48      1.00\n",
-      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8680.12      1.00\n",
-      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.08  11561.50      1.00\n",
-      "  coefs[6]     -0.11      0.29     -0.11     -0.60      0.36   2742.04      1.00\n",
-      "  coefs[7]     -0.47      0.18     -0.47     -0.76     -0.17   2872.73      1.00\n",
-      "  coefs[8]      0.11      0.34      0.11     -0.46      0.65   2724.86      1.00\n",
-      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  11593.39      1.00\n",
-      " coefs[10]      0.46      0.65      0.45     -0.61      1.52   3002.02      1.00\n",
-      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3004.38      1.00\n",
-      " coefs[12]      0.07      0.65      0.06     -0.97      1.17   2999.89      1.00\n",
-      " coefs[13]     -1.05      0.62     -0.99     -2.05     -0.03   4368.86      1.00\n",
-      " coefs[14]     -0.46      0.68     -0.34     -1.53      0.53   5985.35      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.70      0.01   4554.68      1.00\n",
-      " coefs[16]     -0.71      0.60     -0.60     -1.63      0.13   5072.77      1.00\n",
-      " coefs[17]      0.08      0.16      0.08     -0.17      0.35    613.24      1.00\n",
-      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.41   5692.96      1.00\n",
-      " coefs[19]     -0.46      0.68     -0.37     -1.57      0.59   5682.49      1.00\n",
-      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4910.05      1.00\n",
-      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1340.87      1.00\n",
-      " coefs[22]     -0.00      0.07      0.00     -0.12      0.11   1151.16      1.00\n",
-      " coefs[23]      0.19      0.25      0.19     -0.20      0.61    571.15      1.00\n",
-      " coefs[24]      0.07      0.15      0.07     -0.18      0.32    570.76      1.00\n",
-      " coefs[25]     -0.12      0.23     -0.12     -0.52      0.25    570.00      1.00\n",
-      " coefs[26]      0.06      0.18      0.06     -0.24      0.36    570.92      1.00\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.14   4857.10      1.00\n",
-      " coefs[28]      0.03      0.99      0.03     -1.63      1.63  11053.83      1.00\n",
-      " coefs[29]      0.02      0.08      0.02     -0.10      0.15    601.17      1.00\n",
-      " coefs[30]      0.08      0.09      0.08     -0.07      0.22    653.46      1.00\n",
-      " coefs[31]      0.02      0.07      0.02     -0.10      0.14    780.03      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    587.20      1.00\n",
-      " coefs[33]      0.11      0.13      0.11     -0.10      0.33    578.82      1.00\n",
-      " coefs[34]      0.91      0.59      0.78      0.09      1.76   4633.63      1.00\n",
-      " coefs[35]      0.32      0.24      0.32     -0.10      0.70    562.55      1.00\n",
-      " coefs[36]      0.24      0.31      0.24     -0.25      0.78    550.52      1.00\n",
-      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    553.24      1.00\n",
-      " coefs[38]     -0.06      0.04     -0.06     -0.12      0.00    887.46      1.00\n",
-      " coefs[39]      0.04      0.08      0.04     -0.08      0.17    641.10      1.00\n",
-      " coefs[40]      0.09      0.05      0.08      0.00      0.16    677.50      1.00\n",
-      " coefs[41]      0.03      0.05      0.03     -0.06      0.12    940.91      1.00\n",
-      " coefs[42]     -0.06      0.42     -0.06     -0.71      0.66    556.19      1.00\n",
-      " coefs[43]     -0.06      0.23     -0.06     -0.44      0.33    559.39      1.00\n",
-      " coefs[44]      0.14      0.21      0.14     -0.21      0.50    553.46      1.00\n",
-      " coefs[45]      0.07      0.30      0.07     -0.43      0.56    553.47      1.00\n",
-      " coefs[46]      0.20      0.28      0.20     -0.25      0.68    554.58      1.00\n",
-      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    783.37      1.00\n",
-      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    604.14      1.00\n",
-      " coefs[49]     -0.81      0.60     -0.68     -1.69     -0.01   4306.68      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   4711.24      1.00\n",
-      " coefs[51]     -0.16      0.17     -0.16     -0.43      0.13    568.23      1.00\n",
-      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.15    568.33      1.00\n",
-      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    579.79      1.00\n",
-      " coefs[54]     -1.60      0.18     -1.58     -1.89     -1.30   3802.32      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 25 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.02      0.06      2.02      1.91      2.12  10309.61      1.00\n",
-      "  coefs[1]     -0.03      0.03     -0.03     -0.09      0.03  12124.19      1.00\n",
-      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.05   3571.48      1.00\n",
-      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.22   7482.98      1.00\n",
-      "  coefs[4]     -0.14      0.04     -0.14     -0.20     -0.08   8459.79      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10634.42      1.00\n",
-      "  coefs[6]      0.38      0.27      0.38     -0.08      0.82   2778.57      1.00\n",
-      "  coefs[7]     -0.76      0.17     -0.76     -1.02     -0.47   2903.10      1.00\n",
-      "  coefs[8]      0.74      0.32      0.74      0.20      1.26   2757.86      1.00\n",
-      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  12221.01      1.00\n",
-      " coefs[10]      0.41      0.65      0.41     -0.69      1.46   3052.96      1.00\n",
-      " coefs[11]     -0.06      0.29     -0.06     -0.53      0.42   3052.24      1.00\n",
-      " coefs[12]      0.13      0.65      0.12     -0.94      1.21   3059.80      1.00\n",
-      " coefs[13]     -1.04      0.62     -0.98     -2.09     -0.09   4412.03      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.53      0.53   5862.03      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.68     -1.65      0.05   5014.93      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.58     -1.58      0.17   5030.84      1.00\n",
-      " coefs[17]     -0.27      0.23     -0.25     -0.61      0.13   1177.44      1.00\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.43   5614.50      1.00\n",
-      " coefs[19]     -0.43      0.68     -0.34     -1.54      0.61   5929.27      1.00\n",
-      " coefs[20]      0.02      0.97      0.01     -1.48      1.69  12485.30      1.00\n",
-      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1268.53      1.00\n",
-      " coefs[22]      0.06      0.05      0.06     -0.03      0.15    729.52      1.00\n",
-      " coefs[23]      0.19      0.25      0.19     -0.24      0.57    558.82      1.00\n",
-      " coefs[24]      0.05      0.16      0.05     -0.21      0.31    580.78      1.00\n",
-      " coefs[25]     -0.08      0.23     -0.08     -0.50      0.27    548.09      1.00\n",
-      " coefs[26]      0.09      0.18      0.09     -0.22      0.38    547.89      1.00\n",
-      " coefs[27]     -0.70      0.61     -0.58     -1.60      0.15   5096.35      1.00\n",
-      " coefs[28]      0.02      0.99      0.02     -1.66      1.61  10390.05      1.00\n",
-      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    580.62      1.00\n",
-      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    628.19      1.00\n",
-      " coefs[31]     -0.75      0.58     -0.63     -1.62      0.07   4801.85      1.00\n",
-      " coefs[32]      0.09      0.09      0.09     -0.05      0.24    565.21      1.00\n",
-      " coefs[33]      0.15      0.13      0.16     -0.06      0.37    550.40      1.00\n",
-      " coefs[34]      0.09      0.05      0.09      0.01      0.18    895.13      1.00\n",
-      " coefs[35]      0.33      0.24      0.34     -0.07      0.74    535.96      1.00\n",
-      " coefs[36]      0.32      0.31      0.33     -0.19      0.84    533.22      1.00\n",
-      " coefs[37]      0.14      0.20      0.14     -0.20      0.45    537.09      1.00\n",
-      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    939.95      1.00\n",
-      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    647.96      1.00\n",
-      " coefs[40]      0.09      0.06      0.09      0.00      0.18    799.91      1.00\n",
-      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1291.14      1.00\n",
-      " coefs[42]      0.07      0.42      0.08     -0.62      0.77    533.62      1.00\n",
-      " coefs[43]     -0.02      0.23     -0.01     -0.40      0.37    534.58      1.00\n",
-      " coefs[44]      0.16      0.22      0.17     -0.20      0.51    534.54      1.00\n",
-      " coefs[45]      0.09      0.30      0.10     -0.41      0.58    533.79      1.00\n",
-      " coefs[46]      0.22      0.28      0.23     -0.26      0.66    535.06      1.00\n",
-      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    832.04      1.00\n",
-      " coefs[48]     -0.04      0.06     -0.04     -0.15      0.06    617.55      1.00\n",
-      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.01   4879.90      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.73     -1.68     -0.08   4615.40      1.00\n",
-      " coefs[51]     -0.14      0.17     -0.13     -0.43      0.13    546.89      1.00\n",
-      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.16    536.48      1.00\n",
-      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    552.97      1.00\n",
-      " coefs[54]     -1.76      0.19     -1.75     -2.06     -1.45   3911.71      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 26 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.95      0.06      1.95      1.85      2.05   9697.28      1.00\n",
-      "  coefs[1]     -0.01      0.03     -0.01     -0.07      0.04  12200.46      1.00\n",
-      "  coefs[2]     -0.18      0.07     -0.18     -0.28     -0.07   3835.72      1.00\n",
-      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   7753.40      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8914.41      1.00\n",
-      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13   9799.48      1.00\n",
-      "  coefs[6]     -0.44      0.25     -0.44     -0.83     -0.02   3083.93      1.00\n",
-      "  coefs[7]     -0.24      0.15     -0.24     -0.48      0.01   3272.49      1.00\n",
-      "  coefs[8]     -0.25      0.29     -0.24     -0.73      0.22   3069.29      1.00\n",
-      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11351.99      1.00\n",
-      " coefs[10]      0.42      0.65      0.41     -0.72      1.42   3244.67      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.46   3259.76      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -1.05      1.09   3243.82      1.00\n",
-      " coefs[13]     -1.10      0.62     -1.04     -2.07     -0.06   4756.45      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.52   5832.99      1.00\n",
-      " coefs[15]     -0.81      0.57     -0.70     -1.65      0.03   4664.33      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.60     -1.63      0.09   5437.49      1.00\n",
-      " coefs[17]     -0.01      0.17     -0.01     -0.27      0.27    593.91      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   5946.46      1.00\n",
-      " coefs[19]     -0.45      0.69     -0.35     -1.53      0.63   5809.86      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   4961.15      1.00\n",
-      " coefs[21]     -0.77      0.58     -0.65     -1.61      0.02   5202.46      1.00\n",
-      " coefs[22]      0.05      0.05      0.05     -0.03      0.15    658.39      1.00\n",
-      " coefs[23]      0.17      0.25      0.17     -0.23      0.58    514.11      1.00\n",
-      " coefs[24]      0.08      0.16      0.08     -0.17      0.34    523.59      1.00\n",
-      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    507.06      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    507.58      1.00\n",
-      " coefs[27]     -0.73      0.61     -0.60     -1.61      0.13   4905.48      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.60      1.69  10750.90      1.00\n",
-      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    555.98      1.00\n",
-      " coefs[30]      0.01      0.10      0.01     -0.15      0.17    672.45      1.00\n",
-      " coefs[31]      0.01      0.08      0.01     -0.12      0.13    807.56      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    533.46      1.00\n",
-      " coefs[33]      0.16      0.13      0.16     -0.07      0.38    508.16      1.00\n",
-      " coefs[34]      0.93      0.60      0.80      0.11      1.79   4631.74      1.00\n",
-      " coefs[35]      0.30      0.24      0.30     -0.08      0.73    494.20      1.00\n",
-      " coefs[36]      0.34      0.31      0.34     -0.15      0.88    494.83      1.00\n",
-      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    497.12      1.00\n",
-      " coefs[38]      0.04      0.04      0.04     -0.03      0.11    896.21      1.00\n",
-      " coefs[39]     -0.01      0.08     -0.00     -0.14      0.12    622.27      1.00\n",
-      " coefs[40]      0.06      0.05      0.06     -0.01      0.15    578.36      1.00\n",
-      " coefs[41]     -0.78      0.58     -0.66     -1.63      0.03   5017.98      1.00\n",
-      " coefs[42]      0.08      0.42      0.08     -0.62      0.76    493.89      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.34      0.43    499.52      1.00\n",
-      " coefs[44]      0.13      0.22      0.13     -0.21      0.50    496.38      1.00\n",
-      " coefs[45]      0.08      0.30      0.08     -0.44      0.56    492.93      1.00\n",
-      " coefs[46]      0.20      0.28      0.20     -0.28      0.65    498.64      1.00\n",
-      " coefs[47]     -0.82      0.57     -0.71     -1.67     -0.05   4656.06      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    550.33      1.00\n",
-      " coefs[49]     -0.80      0.59     -0.67     -1.65     -0.00   4704.70      1.00\n",
-      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.07   4427.45      1.00\n",
-      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.17    502.20      1.00\n",
-      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    502.02      1.00\n",
-      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    512.18      1.00\n",
-      " coefs[54]     -1.68      0.19     -1.66     -1.96     -1.36   3876.22      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 27 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9664.80      1.00\n",
-      "  coefs[1]     -0.06      0.03     -0.06     -0.11      0.00  12273.76      1.00\n",
-      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3990.60      1.00\n",
-      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   8378.52      1.00\n",
-      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   9122.81      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11   9835.89      1.00\n",
-      "  coefs[6]      0.43      0.28      0.43     -0.05      0.88   3212.70      1.00\n",
-      "  coefs[7]     -0.79      0.17     -0.79     -1.08     -0.52   3328.05      1.00\n",
-      "  coefs[8]      0.87      0.33      0.86      0.31      1.40   3201.38      1.00\n",
-      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  12410.57      1.00\n",
-      " coefs[10]      0.39      0.65      0.38     -0.68      1.46   3077.07      1.00\n",
-      " coefs[11]     -0.06      0.29     -0.06     -0.56      0.40   3088.73      1.00\n",
-      " coefs[12]      0.11      0.65      0.10     -0.94      1.19   3080.15      1.00\n",
-      " coefs[13]     -1.00      0.63     -0.93     -2.05     -0.02   4853.41      1.00\n",
-      " coefs[14]     -0.44      0.67     -0.33     -1.47      0.59   5749.68      1.00\n",
-      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.06   4580.98      1.00\n",
-      " coefs[16]     -0.74      0.58     -0.63     -1.59      0.11   4965.06      1.00\n",
-      " coefs[17]      0.08      0.16      0.08     -0.20      0.33    757.62      1.00\n",
-      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.42   5849.73      1.00\n",
-      " coefs[19]     -0.45      0.66     -0.36     -1.51      0.59   6230.51      1.00\n",
-      " coefs[20]     -0.76      0.59     -0.64     -1.61      0.03   4981.49      1.00\n",
-      " coefs[21]      0.03      0.02      0.03     -0.01      0.07   1097.70      1.00\n",
-      " coefs[22]      0.04      0.06      0.04     -0.05      0.14    997.56      1.00\n",
-      " coefs[23]      0.11      0.25      0.11     -0.31      0.51    703.71      1.00\n",
-      " coefs[24]      0.01      0.16      0.01     -0.27      0.25    725.63      1.00\n",
-      " coefs[25]     -0.05      0.23     -0.05     -0.44      0.32    685.14      1.00\n",
-      " coefs[26]      0.04      0.18      0.04     -0.26      0.33    689.06      1.00\n",
-      " coefs[27]     -0.70      0.63     -0.58     -1.63      0.17   4768.90      1.00\n",
-      " coefs[28]      0.02      1.00      0.03     -1.60      1.70  11348.00      1.00\n",
-      " coefs[29]      0.02      0.08      0.02     -0.11      0.15    782.70      1.00\n",
-      " coefs[30]      0.00      0.10      0.00     -0.17      0.17   1066.32      1.00\n",
-      " coefs[31]     -0.75      0.58     -0.63     -1.61      0.07   4989.76      1.00\n",
-      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    711.07      1.00\n",
-      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    689.21      1.00\n",
-      " coefs[34]      0.15      0.06      0.15      0.04      0.25   1520.05      1.00\n",
-      " coefs[35]      0.35      0.24      0.35     -0.05      0.75    671.45      1.00\n",
-      " coefs[36]      0.37      0.31      0.38     -0.15      0.87    674.78      1.00\n",
-      " coefs[37]      0.16      0.20      0.16     -0.16      0.49    677.33      1.00\n",
-      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    942.01      1.00\n",
-      " coefs[39]     -0.07      0.09     -0.06     -0.21      0.07   1046.12      1.00\n",
-      " coefs[40]      0.05      0.05      0.06     -0.03      0.14    837.95      1.00\n",
-      " coefs[41]     -0.79      0.59     -0.66     -1.65      0.04   5069.57      1.00\n",
-      " coefs[42]      0.09      0.42      0.09     -0.60      0.76    671.11      1.00\n",
-      " coefs[43]      0.01      0.23      0.01     -0.37      0.40    680.37      1.00\n",
-      " coefs[44]      0.17      0.21      0.18     -0.18      0.53    673.74      1.00\n",
-      " coefs[45]      0.12      0.30      0.13     -0.35      0.64    669.63      1.00\n",
-      " coefs[46]      0.25      0.28      0.25     -0.19      0.73    674.48      1.00\n",
-      " coefs[47]     -0.84      0.58     -0.71     -1.70     -0.04   4818.66      1.00\n",
-      " coefs[48]     -0.05      0.06     -0.05     -0.16      0.05    730.24      1.00\n",
-      " coefs[49]     -0.80      0.60     -0.68     -1.65      0.02   4871.11      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.08   4482.28      1.00\n",
-      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    679.51      1.00\n",
-      " coefs[52]     -0.12      0.16     -0.12     -0.39      0.13    679.23      1.00\n",
-      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.08    691.74      1.00\n",
-      " coefs[54]     -1.77      0.19     -1.76     -2.05     -1.45   4110.31      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 28 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.06      0.06      2.06      1.95      2.16  10589.43      1.00\n",
-      "  coefs[1]     -0.01      0.04     -0.01     -0.07      0.05  12371.89      1.00\n",
-      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3405.65      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8382.81      1.00\n",
-      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   9570.33      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11  11024.17      1.00\n",
-      "  coefs[6]      0.43      0.29      0.43     -0.05      0.92   2818.87      1.00\n",
-      "  coefs[7]     -0.81      0.18     -0.80     -1.10     -0.52   2976.70      1.00\n",
-      "  coefs[8]      0.78      0.34      0.77      0.23      1.36   2826.32      1.00\n",
-      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  11133.18      1.00\n",
-      " coefs[10]      0.46      0.65      0.46     -0.62      1.50   3195.00      1.00\n",
-      " coefs[11]     -0.09      0.29     -0.09     -0.56      0.39   3191.49      1.00\n",
-      " coefs[12]      0.07      0.65      0.06     -0.99      1.13   3197.02      1.00\n",
-      " coefs[13]     -0.99      0.63     -0.93     -2.01      0.02   5157.05      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.50      0.55   6122.62      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.67     -1.63      0.08   4822.13      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.60     -1.60      0.12   5059.19      1.00\n",
-      " coefs[17]     -0.10      0.19     -0.09     -0.41      0.20    945.77      1.00\n",
-      " coefs[18]     -0.56      0.66     -0.44     -1.56      0.41   5737.00      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5933.46      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.02   4978.14      1.00\n",
-      " coefs[21]      0.03      0.03      0.03     -0.02      0.07   1257.64      1.00\n",
-      " coefs[22]      0.04      0.06      0.04     -0.05      0.13    949.70      1.00\n",
-      " coefs[23]      0.08      0.24      0.09     -0.31      0.49    632.12      1.00\n",
-      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.24    651.47      1.00\n",
-      " coefs[25]     -0.11      0.23     -0.10     -0.48      0.27    596.53      1.00\n",
-      " coefs[26]      0.04      0.18      0.04     -0.26      0.32    596.33      1.00\n",
-      " coefs[27]     -0.73      0.62     -0.60     -1.63      0.14   5089.50      1.00\n",
-      " coefs[28]      0.02      0.99      0.03     -1.63      1.64  10446.30      1.00\n",
-      " coefs[29]      0.02      0.08      0.02     -0.11      0.14    685.01      1.00\n",
-      " coefs[30]      0.01      0.10      0.01     -0.16      0.17    939.40      1.00\n",
-      " coefs[31]     -0.03      0.10     -0.02     -0.17      0.13   1350.65      1.00\n",
-      " coefs[32]      0.05      0.09      0.05     -0.09      0.20    622.62      1.00\n",
-      " coefs[33]      0.16      0.13      0.16     -0.05      0.38    604.88      1.00\n",
-      " coefs[34]      0.14      0.06      0.13      0.04      0.24   1503.83      1.00\n",
-      " coefs[35]      0.34      0.24      0.34     -0.06      0.72    589.40      1.00\n",
-      " coefs[36]      0.32      0.31      0.33     -0.18      0.83    582.35      1.00\n",
-      " coefs[37]      0.14      0.19      0.15     -0.17      0.46    591.16      1.00\n",
-      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04    968.98      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    743.97      1.00\n",
-      " coefs[40]      0.02      0.05      0.02     -0.06      0.11    730.94      1.00\n",
-      " coefs[41]     -0.80      0.58     -0.68     -1.68     -0.02   5204.80      1.00\n",
-      " coefs[42]      0.01      0.41      0.02     -0.67      0.66    584.43      1.00\n",
-      " coefs[43]     -0.07      0.23     -0.07     -0.44      0.30    588.94      1.00\n",
-      " coefs[44]      0.17      0.21      0.17     -0.18      0.51    582.84      1.00\n",
-      " coefs[45]      0.17      0.29      0.18     -0.32      0.64    585.86      1.00\n",
-      " coefs[46]      0.23      0.27      0.23     -0.25      0.65    586.24      1.00\n",
-      " coefs[47]     -0.12      0.09     -0.11     -0.26      0.02   1237.70      1.00\n",
-      " coefs[48]     -0.09      0.06     -0.09     -0.18      0.02    645.34      1.00\n",
-      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1713.26      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.07   4466.26      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.11     -0.38      0.16    596.53      1.00\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    593.47      1.00\n",
-      " coefs[53]     -0.20      0.13     -0.19     -0.41      0.00    611.55      1.00\n",
-      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.41   4242.11      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 29 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.99      0.06      1.99      1.89      2.09  10281.72      1.00\n",
-      "  coefs[1]     -0.08      0.03     -0.08     -0.14     -0.02  11111.60      1.00\n",
-      "  coefs[2]     -0.11      0.08     -0.11     -0.24      0.02   3283.15      1.00\n",
-      "  coefs[3]     -0.29      0.03     -0.29     -0.34     -0.23   7208.35      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8500.50      1.00\n",
-      "  coefs[5]     -0.10      0.03     -0.10     -0.16     -0.05  11522.62      1.00\n",
-      "  coefs[6]     -0.03      0.33     -0.03     -0.58      0.52   2779.03      1.00\n",
-      "  coefs[7]     -0.49      0.20     -0.49     -0.83     -0.17   2911.34      1.00\n",
-      "  coefs[8]      0.24      0.39      0.24     -0.44      0.85   2776.23      1.00\n",
-      "  coefs[9]     -0.07      0.03     -0.07     -0.11     -0.02  10734.26      1.00\n",
-      " coefs[10]      0.41      0.65      0.41     -0.67      1.45   3176.70      1.00\n",
-      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3179.52      1.00\n",
-      " coefs[12]      0.10      0.65      0.09     -0.97      1.16   3177.55      1.00\n",
-      " coefs[13]     -1.00      0.64     -0.94     -2.00      0.02   4659.78      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.54   5589.40      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.70     -1.67      0.03   4418.25      1.00\n",
-      " coefs[16]     -0.72      0.59     -0.60     -1.61      0.12   5208.44      1.00\n",
-      " coefs[17]     -0.17      0.19     -0.16     -0.47      0.15    943.32      1.00\n",
-      " coefs[18]     -0.57      0.66     -0.45     -1.58      0.39   5903.46      1.00\n",
-      " coefs[19]     -0.47      0.69     -0.38     -1.55      0.61   5385.20      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   5011.82      1.00\n",
-      " coefs[21]      0.04      0.03      0.04     -0.01      0.09   1530.86      1.00\n",
-      " coefs[22]      0.09      0.05      0.09      0.00      0.17    733.93      1.00\n",
-      " coefs[23]      0.04      0.25      0.04     -0.37      0.44    635.37      1.00\n",
-      " coefs[24]     -0.00      0.16     -0.01     -0.27      0.25    647.37      1.00\n",
-      " coefs[25]     -0.14      0.23     -0.14     -0.51      0.26    626.98      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.28      0.32    634.01      1.00\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.16   4950.71      1.00\n",
-      " coefs[28]      0.03      0.99      0.03     -1.58      1.65  10491.51      1.00\n",
-      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    667.60      1.00\n",
-      " coefs[30]      0.04      0.09      0.04     -0.11      0.19    785.86      1.00\n",
-      " coefs[31]      0.04      0.07      0.05     -0.07      0.17    933.56      1.00\n",
-      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    650.23      1.00\n",
-      " coefs[33]      0.20      0.13      0.20     -0.01      0.43    626.70      1.00\n",
-      " coefs[34]      0.92      0.59      0.80      0.11      1.77   4818.61      1.00\n",
-      " coefs[35]      0.31      0.24      0.30     -0.10      0.70    609.88      1.00\n",
-      " coefs[36]      0.31      0.31      0.31     -0.21      0.82    613.54      1.00\n",
-      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    621.85      1.00\n",
-      " coefs[38]     -0.02      0.05     -0.02     -0.11      0.06   1553.81      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    739.41      1.00\n",
-      " coefs[40]      0.10      0.05      0.10      0.01      0.19    890.30      1.00\n",
-      " coefs[41]     -0.01      0.07     -0.00     -0.12      0.10   1456.92      1.00\n",
-      " coefs[42]      0.02      0.42      0.01     -0.67      0.69    613.09      1.00\n",
-      " coefs[43]     -0.00      0.23     -0.01     -0.40      0.37    621.98      1.00\n",
-      " coefs[44]      0.15      0.22      0.15     -0.21      0.50    614.00      1.00\n",
-      " coefs[45]      0.07      0.30      0.07     -0.43      0.55    621.21      1.00\n",
-      " coefs[46]      0.19      0.28      0.19     -0.26      0.66    620.99      1.00\n",
-      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00   1359.24      1.00\n",
-      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    644.79      1.00\n",
-      " coefs[49]     -0.82      0.60     -0.70     -1.68     -0.01   4763.74      1.00\n",
-      " coefs[50]     -0.84      0.59     -0.72     -1.69     -0.06   4904.38      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.15    629.04      1.00\n",
-      " coefs[52]     -0.08      0.16     -0.08     -0.34      0.18    630.19      1.00\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.03    631.24      1.00\n",
-      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.34   3831.89      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 30 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.90      0.06      1.90      1.80      2.00   9019.97      1.00\n",
-      "  coefs[1]     -0.04      0.03     -0.04     -0.10      0.02  10767.61      1.00\n",
-      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3295.95      1.00\n",
-      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7375.50      1.00\n",
-      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   8457.63      1.00\n",
-      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10886.68      1.00\n",
-      "  coefs[6]      0.50      0.29      0.50      0.03      0.97   2663.40      1.00\n",
-      "  coefs[7]     -0.78      0.18     -0.78     -1.08     -0.50   2793.04      1.00\n",
-      "  coefs[8]      0.88      0.34      0.88      0.30      1.41   2672.27      1.00\n",
-      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  10751.40      1.00\n",
-      " coefs[10]      0.42      0.65      0.41     -0.61      1.51   3393.24      1.00\n",
-      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3406.03      1.00\n",
-      " coefs[12]      0.07      0.65      0.07     -0.99      1.13   3403.50      1.00\n",
-      " coefs[13]     -1.01      0.63     -0.95     -2.05     -0.03   4984.38      1.00\n",
-      " coefs[14]     -0.46      0.66     -0.36     -1.47      0.53   5921.21      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.67     -1.64      0.05   4545.78      1.00\n",
-      " coefs[16]     -0.73      0.57     -0.61     -1.58      0.10   5089.11      1.00\n",
-      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17   1126.41      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.41   5515.73      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.57      0.56   5501.46      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   5123.43      1.00\n",
-      " coefs[21]     -0.76      0.59     -0.64     -1.61      0.05   4825.12      1.00\n",
-      " coefs[22]      0.02      0.07      0.03     -0.10      0.14   1548.35      1.00\n",
-      " coefs[23]      0.05      0.25      0.06     -0.35      0.47    783.10      1.00\n",
-      " coefs[24]      0.08      0.16      0.09     -0.16      0.35    779.21      1.00\n",
-      " coefs[25]     -0.10      0.23     -0.09     -0.49      0.28    756.44      1.00\n",
-      " coefs[26]     -0.00      0.18      0.00     -0.29      0.31    755.12      1.00\n",
-      " coefs[27]     -0.71      0.63     -0.58     -1.63      0.17   4745.70      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.54      1.73   9981.61      1.00\n",
-      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    854.92      1.00\n",
-      " coefs[30]     -0.09      0.13     -0.08     -0.28      0.13   1528.49      1.00\n",
-      " coefs[31]     -0.76      0.58     -0.64     -1.61      0.07   4759.95      1.00\n",
-      " coefs[32]      0.13      0.09      0.13     -0.02      0.27    775.07      1.00\n",
-      " coefs[33]      0.16      0.13      0.16     -0.05      0.39    764.75      1.00\n",
-      " coefs[34]      0.91      0.60      0.79      0.08      1.76   4523.52      1.00\n",
-      " coefs[35]      0.37      0.24      0.37     -0.02      0.79    745.02      1.01\n",
-      " coefs[36]      0.35      0.31      0.35     -0.13      0.90    743.92      1.00\n",
-      " coefs[37]      0.19      0.20      0.20     -0.13      0.52    747.52      1.00\n",
-      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04   1238.03      1.00\n",
-      " coefs[39]      0.01      0.08      0.02     -0.11      0.14    874.10      1.00\n",
-      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    917.48      1.00\n",
-      " coefs[41]      0.01      0.05      0.01     -0.08      0.10   1128.55      1.00\n",
-      " coefs[42]      0.05      0.41      0.05     -0.64      0.74    740.73      1.00\n",
-      " coefs[43]     -0.04      0.23     -0.04     -0.41      0.36    744.09      1.00\n",
-      " coefs[44]      0.18      0.21      0.18     -0.16      0.55    748.09      1.00\n",
-      " coefs[45]      0.15      0.30      0.16     -0.32      0.67    742.57      1.00\n",
-      " coefs[46]      0.21      0.28      0.22     -0.24      0.68    748.05      1.00\n",
-      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05   1192.87      1.00\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    845.74      1.00\n",
-      " coefs[49]     -0.79      0.60     -0.68     -1.65      0.01   5087.76      1.00\n",
-      " coefs[50]     -0.85      0.59     -0.72     -1.69     -0.05   4519.70      1.00\n",
-      " coefs[51]     -0.09      0.17     -0.08     -0.37      0.19    749.63      1.00\n",
-      " coefs[52]     -0.09      0.16     -0.09     -0.38      0.15    752.57      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.13     -0.36      0.07    766.61      1.00\n",
-      " coefs[54]     -1.70      0.19     -1.69     -2.00     -1.40   4002.84      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 31 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.00      0.06      2.00      1.89      2.10  10506.43      1.00\n",
-      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11576.31      1.00\n",
-      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.03   3713.76      1.00\n",
-      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   8843.21      1.00\n",
-      "  coefs[4]     -0.05      0.04     -0.05     -0.10      0.01   9500.03      1.00\n",
-      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10864.35      1.00\n",
-      "  coefs[6]      0.33      0.27      0.32     -0.10      0.76   2852.16      1.00\n",
-      "  coefs[7]     -0.76      0.16     -0.75     -1.01     -0.48   2964.01      1.00\n",
-      "  coefs[8]      0.69      0.31      0.68      0.19      1.20   2847.07      1.00\n",
-      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11519.52      1.00\n",
-      " coefs[10]      0.39      0.65      0.39     -0.70      1.46   3245.63      1.00\n",
-      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3261.90      1.00\n",
-      " coefs[12]      0.11      0.65      0.11     -0.92      1.23   3256.33      1.00\n",
-      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   5056.56      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.49      0.54   6112.69      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.68     -1.60      0.08   4585.07      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.61     -1.61      0.11   5040.88      1.00\n",
-      " coefs[17]     -0.26      0.23     -0.25     -0.62      0.12   1111.71      1.00\n",
-      " coefs[18]     -0.54      0.66     -0.42     -1.56      0.42   5994.44      1.00\n",
-      " coefs[19]     -0.45      0.67     -0.35     -1.57      0.57   5768.92      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.01   5062.81      1.00\n",
-      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.02   5297.12      1.00\n",
-      " coefs[22]      0.06      0.06      0.06     -0.04      0.16    832.32      1.00\n",
-      " coefs[23]      0.14      0.25      0.14     -0.27      0.54    553.00      1.01\n",
-      " coefs[24]      0.09      0.16      0.09     -0.18      0.33    554.02      1.01\n",
-      " coefs[25]     -0.12      0.24     -0.12     -0.51      0.26    538.13      1.01\n",
-      " coefs[26]      0.03      0.18      0.03     -0.28      0.32    545.03      1.01\n",
-      " coefs[27]     -0.68      0.63     -0.56     -1.63      0.18   4961.27      1.00\n",
-      " coefs[28]      0.03      0.99      0.03     -1.62      1.65  10677.03      1.00\n",
-      " coefs[29]      0.09      0.08      0.09     -0.04      0.22    593.65      1.01\n",
-      " coefs[30]      0.07      0.09      0.07     -0.08      0.21    650.49      1.01\n",
-      " coefs[31]     -0.02      0.10     -0.02     -0.18      0.13   1189.70      1.00\n",
-      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    571.81      1.01\n",
-      " coefs[33]      0.16      0.13      0.16     -0.06      0.38    540.11      1.01\n",
-      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1289.56      1.00\n",
-      " coefs[35]      0.35      0.25      0.35     -0.06      0.74    528.74      1.01\n",
-      " coefs[36]      0.31      0.31      0.31     -0.22      0.81    527.93      1.01\n",
-      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    535.58      1.01\n",
-      " coefs[38]     -0.82      0.58     -0.69     -1.66     -0.03   5038.93      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    632.38      1.01\n",
-      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    644.97      1.01\n",
-      " coefs[41]     -0.79      0.59     -0.67     -1.66      0.03   4898.98      1.00\n",
-      " coefs[42]      0.04      0.42      0.05     -0.68      0.69    530.13      1.01\n",
-      " coefs[43]      0.00      0.23      0.01     -0.38      0.38    535.88      1.01\n",
-      " coefs[44]      0.18      0.22      0.18     -0.19      0.52    531.17      1.01\n",
-      " coefs[45]      0.11      0.30      0.11     -0.39      0.60    527.06      1.01\n",
-      " coefs[46]      0.26      0.28      0.26     -0.21      0.71    527.83      1.01\n",
-      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    742.72      1.01\n",
-      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    592.25      1.01\n",
-      " coefs[49]     -0.80      0.59     -0.68     -1.65      0.01   4900.71      1.00\n",
-      " coefs[50]     -0.87      0.58     -0.75     -1.71     -0.09   4640.27      1.00\n",
-      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.16    539.58      1.01\n",
-      " coefs[52]     -0.10      0.16     -0.10     -0.38      0.15    540.36      1.01\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    553.93      1.01\n",
-      " coefs[54]     -1.79      0.19     -1.77     -2.09     -1.49   4183.29      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 32 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.04      0.06      2.04      1.93      2.14  10125.47      1.00\n",
-      "  coefs[1]     -0.03      0.04     -0.03     -0.09      0.03  11574.62      1.00\n",
-      "  coefs[2]     -0.05      0.08     -0.05     -0.17      0.08   3281.43      1.00\n",
-      "  coefs[3]     -0.35      0.03     -0.35     -0.41     -0.29   7593.31      1.00\n",
-      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8084.89      1.00\n",
-      "  coefs[5]     -0.13      0.03     -0.13     -0.19     -0.08  10905.67      1.00\n",
-      "  coefs[6]     -0.31      0.31     -0.30     -0.82      0.18   2706.12      1.00\n",
-      "  coefs[7]     -0.31      0.19     -0.31     -0.64     -0.02   2873.98      1.00\n",
-      "  coefs[8]     -0.05      0.36     -0.04     -0.64      0.54   2711.99      1.00\n",
-      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.01  11662.00      1.00\n",
-      " coefs[10]      0.36      0.65      0.35     -0.70      1.45   3104.82      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3113.43      1.00\n",
-      " coefs[12]      0.13      0.65      0.11     -0.91      1.23   3110.90      1.00\n",
-      " coefs[13]     -0.92      0.65     -0.85     -1.98      0.10   4557.60      1.00\n",
-      " coefs[14]     -0.48      0.67     -0.37     -1.53      0.52   5472.45      1.00\n",
-      " coefs[15]     -0.77      0.57     -0.67     -1.66      0.05   4497.69      1.00\n",
-      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.10   5133.58      1.00\n",
-      " coefs[17]     -0.19      0.19     -0.18     -0.49      0.11    650.98      1.00\n",
-      " coefs[18]     -0.56      0.66     -0.45     -1.58      0.38   5533.20      1.00\n",
-      " coefs[19]     -0.48      0.68     -0.39     -1.60      0.56   5797.66      1.00\n",
-      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5225.53      1.00\n",
-      " coefs[21]      0.85      0.59      0.73      0.05      1.69   4743.33      1.00\n",
-      " coefs[22]      0.08      0.06      0.08     -0.01      0.17    616.41      1.00\n",
-      " coefs[23]     -0.12      0.26     -0.12     -0.55      0.27    509.35      1.00\n",
-      " coefs[24]      0.01      0.16      0.01     -0.26      0.26    505.07      1.00\n",
-      " coefs[25]     -0.06      0.23     -0.06     -0.46      0.31    470.64      1.00\n",
-      " coefs[26]     -0.01      0.18     -0.01     -0.32      0.28    466.27      1.00\n",
-      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.11   4885.26      1.00\n",
-      " coefs[28]      0.02      1.00      0.03     -1.53      1.77  10588.75      1.00\n",
-      " coefs[29]      0.06      0.08      0.06     -0.07      0.18    499.21      1.00\n",
-      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    651.77      1.00\n",
-      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13    974.28      1.00\n",
-      " coefs[32]      0.13      0.09      0.13     -0.02      0.28    487.05      1.00\n",
-      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    456.31      1.00\n",
-      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4689.58      1.00\n",
-      " coefs[35]      0.36      0.24      0.36     -0.03      0.77    458.75      1.00\n",
-      " coefs[36]      0.36      0.31      0.36     -0.15      0.86    453.29      1.00\n",
-      " coefs[37]      0.13      0.20      0.13     -0.18      0.46    457.34      1.00\n",
-      " coefs[38]      0.00      0.05      0.01     -0.08      0.09   1270.06      1.00\n",
-      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    528.49      1.00\n",
-      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    533.76      1.00\n",
-      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1041.39      1.00\n",
-      " coefs[42]      0.09      0.42      0.08     -0.61      0.74    455.70      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.35      0.40    460.85      1.00\n",
-      " coefs[44]      0.14      0.22      0.15     -0.22      0.49    447.48      1.00\n",
-      " coefs[45]      0.10      0.30      0.10     -0.39      0.58    452.15      1.00\n",
-      " coefs[46]      0.17      0.28      0.17     -0.28      0.63    450.76      1.00\n",
-      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00    959.11      1.00\n",
-      " coefs[48]     -0.04      0.06     -0.04     -0.14      0.07    493.15      1.00\n",
-      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.01   4845.43      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4590.09      1.00\n",
-      " coefs[51]     -0.14      0.17     -0.15     -0.43      0.12    466.09      1.00\n",
-      " coefs[52]     -0.11      0.16     -0.11     -0.37      0.15    465.86      1.00\n",
-      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    473.04      1.00\n",
-      " coefs[54]     -1.67      0.19     -1.66     -1.97     -1.36   4072.51      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 33 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.91      0.06      1.91      1.81      2.01  10511.47      1.00\n",
-      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12220.55      1.00\n",
-      "  coefs[2]     -0.07      0.07     -0.07     -0.19      0.04   3687.76      1.00\n",
-      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   7665.75      1.00\n",
-      "  coefs[4]     -0.06      0.03     -0.06     -0.11     -0.00   9077.63      1.00\n",
-      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  11684.74      1.00\n",
-      "  coefs[6]      0.26      0.29      0.25     -0.20      0.75   2923.46      1.00\n",
-      "  coefs[7]     -0.61      0.18     -0.61     -0.89     -0.31   3050.64      1.00\n",
-      "  coefs[8]      0.61      0.34      0.60      0.07      1.20   2919.52      1.00\n",
-      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11351.45      1.00\n",
-      " coefs[10]      0.39      0.65      0.38     -0.73      1.41   3228.80      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.41   3241.45      1.00\n",
-      " coefs[12]      0.11      0.64      0.11     -1.00      1.13   3238.02      1.00\n",
-      " coefs[13]     -0.97      0.64     -0.91     -1.98      0.07   5249.99      1.00\n",
-      " coefs[14]     -0.47      0.66     -0.37     -1.48      0.54   6066.89      1.00\n",
-      " coefs[15]     -0.77      0.56     -0.67     -1.64      0.04   4986.07      1.00\n",
-      " coefs[16]     -0.73      0.58     -0.62     -1.61      0.09   5444.07      1.00\n",
-      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17    776.12      1.00\n",
-      " coefs[18]     -0.53      0.67     -0.42     -1.55      0.44   6209.21      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.39     -1.57      0.55   6230.36      1.00\n",
-      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   5067.27      1.00\n",
-      " coefs[21]     -0.76      0.58     -0.65     -1.59      0.05   5458.41      1.00\n",
-      " coefs[22]     -0.00      0.07      0.00     -0.12      0.12   1121.18      1.00\n",
-      " coefs[23]      0.03      0.25      0.04     -0.37      0.44    541.73      1.00\n",
-      " coefs[24]      0.02      0.16      0.02     -0.24      0.27    539.71      1.00\n",
-      " coefs[25]     -0.05      0.23     -0.06     -0.43      0.33    515.63      1.00\n",
-      " coefs[26]      0.05      0.18      0.05     -0.24      0.35    517.55      1.00\n",
-      " coefs[27]     -0.72      0.61     -0.59     -1.60      0.15   5250.27      1.00\n",
-      " coefs[28]      0.02      0.99      0.03     -1.58      1.68  11408.51      1.00\n",
-      " coefs[29]      0.10      0.08      0.10     -0.03      0.22    537.16      1.00\n",
-      " coefs[30]      0.03      0.09      0.04     -0.11      0.18    614.05      1.00\n",
-      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1169.25      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    546.97      1.00\n",
-      " coefs[33]      0.17      0.13      0.17     -0.04      0.39    519.49      1.00\n",
-      " coefs[34]      0.92      0.59      0.80      0.11      1.76   4777.97      1.00\n",
-      " coefs[35]      0.37      0.25      0.37     -0.01      0.78    501.98      1.00\n",
-      " coefs[36]      0.36      0.31      0.36     -0.17      0.85    498.97      1.00\n",
-      " coefs[37]      0.20      0.20      0.20     -0.13      0.51    509.05      1.00\n",
-      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.04    846.24      1.00\n",
-      " coefs[39]     -0.02      0.08     -0.02     -0.14      0.12    639.66      1.00\n",
-      " coefs[40]      0.02      0.05      0.02     -0.06      0.10    608.38      1.00\n",
-      " coefs[41]     -0.80      0.59     -0.68     -1.66      0.01   4980.95      1.00\n",
-      " coefs[42]      0.09      0.42      0.09     -0.57      0.79    505.92      1.00\n",
-      " coefs[43]      0.01      0.23      0.00     -0.37      0.39    510.07      1.00\n",
-      " coefs[44]      0.17      0.22      0.17     -0.17      0.53    501.53      1.00\n",
-      " coefs[45]      0.08      0.30      0.08     -0.42      0.56    499.88      1.00\n",
-      " coefs[46]      0.19      0.28      0.19     -0.29      0.62    505.21      1.00\n",
-      " coefs[47]     -0.86      0.57     -0.74     -1.70     -0.06   4649.67      1.00\n",
-      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    529.40      1.00\n",
-      " coefs[49]      0.04      1.00      0.02     -1.59      1.66  12157.87      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.73     -1.71     -0.08   4732.51      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.16    504.47      1.00\n",
-      " coefs[52]     -0.08      0.16     -0.08     -0.33      0.19    511.03      1.00\n",
-      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.07    515.84      1.00\n",
-      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4097.08      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 34 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.05      0.06      2.05      1.95      2.16  10000.30      1.00\n",
-      "  coefs[1]     -0.02      0.04     -0.01     -0.07      0.05  10626.97      1.00\n",
-      "  coefs[2]     -0.14      0.07     -0.14     -0.26     -0.02   3772.39      1.00\n",
-      "  coefs[3]     -0.36      0.03     -0.36     -0.41     -0.30   7420.44      1.00\n",
-      "  coefs[4]     -0.05      0.03     -0.05     -0.11      0.01   8047.09      1.00\n",
-      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  10672.51      1.00\n",
-      "  coefs[6]     -0.17      0.28     -0.17     -0.63      0.30   3074.31      1.00\n",
-      "  coefs[7]     -0.40      0.17     -0.40     -0.69     -0.13   3264.91      1.00\n",
-      "  coefs[8]      0.07      0.33      0.07     -0.46      0.63   3067.33      1.00\n",
-      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11678.49      1.00\n",
-      " coefs[10]      0.45      0.65      0.44     -0.61      1.54   3198.32      1.00\n",
-      " coefs[11]     -0.06      0.29     -0.06     -0.57      0.39   3220.36      1.00\n",
-      " coefs[12]      0.08      0.65      0.08     -1.01      1.14   3215.87      1.00\n",
-      " coefs[13]     -1.07      0.62     -1.01     -2.06     -0.07   4551.88      1.00\n",
-      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.54   6254.49      1.00\n",
-      " coefs[15]     -0.80      0.57     -0.69     -1.63      0.06   4416.51      1.00\n",
-      " coefs[16]     -0.71      0.59     -0.60     -1.60      0.13   4831.45      1.00\n",
-      " coefs[17]      0.01      0.17      0.01     -0.26      0.28    591.23      1.00\n",
-      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   6005.73      1.00\n",
-      " coefs[19]     -0.45      0.69     -0.36     -1.53      0.63   5509.96      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5084.54      1.00\n",
-      " coefs[21]      0.05      0.03      0.04     -0.01      0.10   1382.99      1.00\n",
-      " coefs[22]      0.10      0.05      0.10      0.02      0.19    596.70      1.00\n",
-      " coefs[23]      0.12      0.25      0.12     -0.30      0.51    508.75      1.00\n",
-      " coefs[24]      0.03      0.16      0.03     -0.23      0.28    514.96      1.00\n",
-      " coefs[25]     -0.10      0.24     -0.11     -0.49      0.27    492.31      1.00\n",
-      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    498.67      1.00\n",
-      " coefs[27]     -0.71      0.61     -0.60     -1.61      0.13   4956.76      1.00\n",
-      " coefs[28]      0.01      0.99      0.01     -1.54      1.69  11010.12      1.00\n",
-      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    556.65      1.00\n",
-      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    614.00      1.00\n",
-      " coefs[31]      0.01      0.08      0.01     -0.12      0.14    795.57      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    512.23      1.00\n",
-      " coefs[33]      0.13      0.13      0.13     -0.09      0.35    502.30      1.00\n",
-      " coefs[34]      0.91      0.59      0.80      0.12      1.77   4902.15      1.00\n",
-      " coefs[35]      0.30      0.25      0.29     -0.11      0.70    491.25      1.00\n",
-      " coefs[36]      0.32      0.32      0.32     -0.20      0.82    483.51      1.00\n",
-      " coefs[37]      0.16      0.20      0.16     -0.17      0.47    490.31      1.00\n",
-      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.03    803.24      1.00\n",
-      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    590.41      1.00\n",
-      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    588.34      1.00\n",
-      " coefs[41]      0.01      0.07      0.01     -0.10      0.12   1292.79      1.00\n",
-      " coefs[42]     -0.02      0.42     -0.02     -0.71      0.65    487.70      1.00\n",
-      " coefs[43]     -0.03      0.23     -0.04     -0.42      0.34    497.84      1.00\n",
-      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    490.22      1.00\n",
-      " coefs[45]      0.10      0.30      0.10     -0.39      0.60    486.10      1.00\n",
-      " coefs[46]      0.20      0.28      0.20     -0.27      0.64    490.41      1.00\n",
-      " coefs[47]     -0.86      0.56     -0.75     -1.70     -0.08   4880.99      1.00\n",
-      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.05    543.91      1.00\n",
-      " coefs[49]     -0.81      0.60     -0.70     -1.66      0.01   4856.94      1.00\n",
-      " coefs[50]     -0.84      0.59     -0.72     -1.70     -0.06   4479.77      1.00\n",
-      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.12    499.77      1.00\n",
-      " coefs[52]     -0.12      0.16     -0.13     -0.38      0.14    497.92      1.00\n",
-      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    497.46      1.00\n",
-      " coefs[54]     -1.64      0.18     -1.62     -1.92     -1.33   3835.59      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 35 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.97      0.06      1.97      1.87      2.07   9742.14      1.00\n",
-      "  coefs[1]     -0.06      0.04     -0.06     -0.12     -0.00  10941.17      1.00\n",
-      "  coefs[2]     -0.15      0.07     -0.15     -0.27     -0.04   3797.76      1.00\n",
-      "  coefs[3]     -0.37      0.03     -0.37     -0.42     -0.31   7795.70      1.00\n",
-      "  coefs[4]     -0.03      0.03     -0.03     -0.09      0.03   8579.09      1.00\n",
-      "  coefs[5]     -0.18      0.03     -0.18     -0.24     -0.13  10418.88      1.00\n",
-      "  coefs[6]      0.05      0.28      0.05     -0.39      0.52   2999.81      1.00\n",
-      "  coefs[7]     -0.57      0.17     -0.57     -0.85     -0.29   3099.11      1.00\n",
-      "  coefs[8]      0.46      0.33      0.46     -0.08      0.99   3002.13      1.00\n",
-      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  10895.90      1.00\n",
-      " coefs[10]      0.47      0.64      0.48     -0.58      1.53   3303.11      1.00\n",
-      " coefs[11]     -0.02      0.29     -0.02     -0.49      0.44   3312.49      1.00\n",
-      " coefs[12]      0.07      0.64      0.07     -1.00      1.10   3315.68      1.00\n",
-      " coefs[13]     -1.07      0.61     -1.00     -2.06     -0.09   4977.49      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.45      0.58   5820.49      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.67     -1.65      0.06   4544.59      1.00\n",
-      " coefs[16]     -0.72      0.58     -0.60     -1.59      0.10   4799.76      1.00\n",
-      " coefs[17]      0.03      0.16      0.04     -0.24      0.30    739.13      1.01\n",
-      " coefs[18]     -0.53      0.66     -0.41     -1.58      0.40   6011.13      1.00\n",
-      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.56   5503.24      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.63      0.02   4644.05      1.00\n",
-      " coefs[21]     -0.78      0.58     -0.66     -1.63      0.01   4745.88      1.00\n",
-      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    873.25      1.01\n",
-      " coefs[23]      0.09      0.25      0.09     -0.31      0.51    688.44      1.01\n",
-      " coefs[24]      0.03      0.16      0.03     -0.22      0.30    737.69      1.01\n",
-      " coefs[25]     -0.05      0.23     -0.04     -0.42      0.36    662.47      1.01\n",
-      " coefs[26]      0.05      0.18      0.06     -0.24      0.36    675.97      1.01\n",
-      " coefs[27]     -0.71      0.61     -0.59     -1.61      0.11   4795.73      1.00\n",
-      " coefs[28]      0.02      1.00      0.02     -1.61      1.69  10020.48      1.00\n",
-      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    720.56      1.01\n",
-      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    833.72      1.01\n",
-      " coefs[31]      0.02      0.08      0.02     -0.11      0.15   1020.81      1.00\n",
-      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    684.55      1.01\n",
-      " coefs[33]      0.14      0.13      0.14     -0.07      0.36    677.90      1.01\n",
-      " coefs[34]      0.13      0.06      0.12      0.03      0.23   1738.80      1.00\n",
-      " coefs[35]      0.28      0.24      0.29     -0.13      0.67    646.54      1.01\n",
-      " coefs[36]      0.28      0.31      0.29     -0.23      0.81    657.65      1.01\n",
-      " coefs[37]      0.21      0.20      0.21     -0.11      0.54    652.29      1.01\n",
-      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    862.31      1.01\n",
-      " coefs[39]     -0.02      0.08     -0.02     -0.15      0.12    869.75      1.01\n",
-      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    755.29      1.01\n",
-      " coefs[41]      0.03      0.05      0.03     -0.06      0.12   1142.51      1.00\n",
-      " coefs[42]     -0.00      0.42      0.00     -0.67      0.72    652.36      1.01\n",
-      " coefs[43]     -0.02      0.23     -0.02     -0.41      0.36    663.81      1.01\n",
-      " coefs[44]      0.14      0.22      0.14     -0.22      0.50    651.86      1.01\n",
-      " coefs[45]      0.07      0.30      0.07     -0.44      0.56    654.79      1.01\n",
-      " coefs[46]      0.19      0.28      0.20     -0.25      0.68    656.43      1.01\n",
-      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05    993.49      1.00\n",
-      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    734.51      1.01\n",
-      " coefs[49]     -0.79      0.60     -0.67     -1.64      0.03   4950.47      1.00\n",
-      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.08   4526.96      1.00\n",
-      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.15    668.74      1.01\n",
-      " coefs[52]     -0.12      0.16     -0.11     -0.38      0.15    669.40      1.01\n",
-      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    676.97      1.01\n",
-      " coefs[54]     -1.65      0.18     -1.64     -1.93     -1.34   4116.09      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 36 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.96      0.06      1.96      1.86      2.06   9372.47      1.00\n",
-      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  10822.01      1.00\n",
-      "  coefs[2]     -0.17      0.06     -0.17     -0.27     -0.07   3864.52      1.00\n",
-      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   7410.99      1.00\n",
-      "  coefs[4]     -0.05      0.03     -0.05     -0.10      0.01   8105.01      1.00\n",
-      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.06  10915.47      1.00\n",
-      "  coefs[6]     -0.03      0.22     -0.03     -0.40      0.33   2760.58      1.00\n",
-      "  coefs[7]     -0.48      0.13     -0.48     -0.69     -0.26   3090.19      1.00\n",
-      "  coefs[8]      0.28      0.25      0.27     -0.12      0.72   2820.91      1.00\n",
-      "  coefs[9]     -0.02      0.03     -0.02     -0.07      0.03  11238.51      1.00\n",
-      " coefs[10]      0.40      0.65      0.40     -0.71      1.44   3232.80      1.00\n",
-      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3242.27      1.00\n",
-      " coefs[12]      0.12      0.65      0.11     -0.97      1.18   3245.95      1.00\n",
-      " coefs[13]     -1.05      0.63     -1.00     -2.09     -0.07   5192.61      1.00\n",
-      " coefs[14]     -0.44      0.68     -0.33     -1.49      0.58   5836.55      1.00\n",
-      " coefs[15]     -0.79      0.57     -0.69     -1.65      0.04   4569.53      1.00\n",
-      " coefs[16]     -0.73      0.59     -0.62     -1.65      0.09   5300.47      1.00\n",
-      " coefs[17]     -0.02      0.17     -0.02     -0.29      0.28    807.36      1.01\n",
-      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5962.50      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.38     -1.57      0.57   5232.08      1.00\n",
-      " coefs[20]      0.02      0.98      0.03     -1.59      1.63  12107.78      1.00\n",
-      " coefs[21]     -0.77      0.60     -0.64     -1.63      0.05   4698.56      1.00\n",
-      " coefs[22]      0.08      0.05      0.08     -0.00      0.17    756.90      1.01\n",
-      " coefs[23]      0.11      0.26      0.11     -0.32      0.52    701.29      1.01\n",
-      " coefs[24]      0.06      0.16      0.06     -0.21      0.31    635.73      1.01\n",
-      " coefs[25]     -0.06      0.24     -0.06     -0.48      0.31    644.03      1.01\n",
-      " coefs[26]     -0.01      0.19     -0.01     -0.31      0.30    665.28      1.01\n",
-      " coefs[27]     -0.72      0.61     -0.61     -1.59      0.12   5029.47      1.00\n",
-      " coefs[28]      0.03      1.00      0.02     -1.63      1.65  10008.37      1.00\n",
-      " coefs[29]      0.01      0.08      0.01     -0.12      0.15    712.05      1.01\n",
-      " coefs[30]      0.03      0.09      0.03     -0.12      0.18    801.77      1.01\n",
-      " coefs[31]     -0.05      0.10     -0.05     -0.20      0.11   1444.46      1.01\n",
-      " coefs[32]      0.13      0.09      0.13     -0.03      0.27    721.44      1.01\n",
-      " coefs[33]      0.11      0.14      0.12     -0.12      0.32    656.94      1.01\n",
-      " coefs[34]      0.91      0.60      0.78      0.09      1.79   4477.44      1.00\n",
-      " coefs[35]      0.29      0.25      0.29     -0.14      0.68    652.55      1.01\n",
-      " coefs[36]      0.30      0.32      0.30     -0.27      0.78    645.31      1.01\n",
-      " coefs[37]      0.12      0.20      0.13     -0.22      0.44    649.06      1.01\n",
-      " coefs[38]      0.00      0.03      0.00     -0.06      0.06    814.07      1.01\n",
-      " coefs[39]     -0.01      0.08     -0.01     -0.15      0.13    885.40      1.01\n",
-      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    786.68      1.01\n",
-      " coefs[41]      0.01      0.06      0.01     -0.08      0.10   1079.71      1.01\n",
-      " coefs[42]      0.03      0.43      0.03     -0.71      0.69    657.11      1.01\n",
-      " coefs[43]     -0.04      0.24     -0.04     -0.45      0.34    660.02      1.01\n",
-      " coefs[44]      0.12      0.22      0.12     -0.26      0.46    643.07      1.01\n",
-      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    656.44      1.01\n",
-      " coefs[46]      0.22      0.29      0.22     -0.26      0.68    652.23      1.01\n",
-      " coefs[47]     -0.05      0.07     -0.05     -0.17      0.07   1065.65      1.01\n",
-      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    689.46      1.01\n",
-      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4683.36      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4867.74      1.00\n",
-      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.16    682.73      1.01\n",
-      " coefs[52]     -0.14      0.17     -0.14     -0.43      0.11    670.78      1.01\n",
-      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.05    678.49      1.01\n",
-      " coefs[54]     -1.63      0.18     -1.61     -1.92     -1.32   3991.08      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 37 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.02      0.06      2.02      1.92      2.12  10190.29      1.00\n",
-      "  coefs[1]      0.03      0.04      0.03     -0.03      0.09  11618.83      1.00\n",
-      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.04   3901.96      1.00\n",
-      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   8168.46      1.00\n",
-      "  coefs[4]     -0.06      0.04     -0.06     -0.12     -0.00   9352.54      1.00\n",
-      "  coefs[5]     -0.17      0.03     -0.17     -0.23     -0.12  11575.01      1.00\n",
-      "  coefs[6]      0.44      0.27      0.42     -0.00      0.87   3054.71      1.00\n",
-      "  coefs[7]     -0.85      0.16     -0.84     -1.11     -0.58   3227.23      1.00\n",
-      "  coefs[8]      0.81      0.31      0.80      0.29      1.31   3054.83      1.00\n",
-      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11497.32      1.00\n",
-      " coefs[10]      0.43      0.65      0.42     -0.66      1.50   3059.84      1.00\n",
-      " coefs[11]     -0.07      0.29     -0.08     -0.57      0.39   3069.11      1.00\n",
-      " coefs[12]      0.05      0.65      0.04     -1.03      1.12   3065.23      1.00\n",
-      " coefs[13]     -0.95      0.64     -0.89     -1.95      0.10   5155.64      1.00\n",
-      " coefs[14]     -0.45      0.67     -0.34     -1.46      0.60   6013.74      1.00\n",
-      " coefs[15]     -0.76      0.58     -0.65     -1.62      0.10   4813.79      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.58     -1.57      0.16   5147.70      1.00\n",
-      " coefs[17]     -0.85      0.55     -0.76     -1.68     -0.01   4545.60      1.00\n",
-      " coefs[18]     -0.56      0.66     -0.43     -1.54      0.44   6040.82      1.00\n",
-      " coefs[19]     -0.47      0.67     -0.37     -1.57      0.55   6180.31      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.04   5180.47      1.00\n",
-      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5257.24      1.00\n",
-      " coefs[22]      0.04      0.06      0.04     -0.06      0.13    996.95      1.00\n",
-      " coefs[23]      0.05      0.24      0.05     -0.38      0.42    686.43      1.00\n",
-      " coefs[24]      0.14      0.15      0.14     -0.12      0.38    671.57      1.00\n",
-      " coefs[25]     -0.12      0.23     -0.11     -0.49      0.26    670.77      1.00\n",
-      " coefs[26]      0.11      0.18      0.12     -0.18      0.39    661.76      1.00\n",
-      " coefs[27]     -0.70      0.62     -0.59     -1.60      0.17   5031.16      1.00\n",
-      " coefs[28]      0.02      1.00      0.02     -1.63      1.68  10507.75      1.00\n",
-      " coefs[29]      0.03      0.08      0.03     -0.10      0.16    760.67      1.00\n",
-      " coefs[30]      0.10      0.09      0.10     -0.05      0.24    811.00      1.00\n",
-      " coefs[31]     -0.76      0.59     -0.63     -1.60      0.08   4563.06      1.00\n",
-      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    686.24      1.00\n",
-      " coefs[33]      0.18      0.13      0.18     -0.03      0.39    665.40      1.00\n",
-      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4500.21      1.00\n",
-      " coefs[35]      0.39      0.24      0.40     -0.02      0.76    645.92      1.00\n",
-      " coefs[36]      0.43      0.31      0.43     -0.11      0.90    646.61      1.00\n",
-      " coefs[37]      0.20      0.19      0.20     -0.13      0.50    649.74      1.00\n",
-      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    945.88      1.00\n",
-      " coefs[39]      0.04      0.08      0.04     -0.09      0.16    786.82      1.00\n",
-      " coefs[40]      0.12      0.05      0.12      0.03      0.20    849.33      1.00\n",
-      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   5036.10      1.00\n",
-      " coefs[42]      0.02      0.41      0.03     -0.70      0.64    646.14      1.00\n",
-      " coefs[43]      0.01      0.23      0.01     -0.39      0.36    650.33      1.00\n",
-      " coefs[44]      0.23      0.21      0.23     -0.16      0.53    641.32      1.00\n",
-      " coefs[45]      0.16      0.29      0.17     -0.35      0.62    645.40      1.00\n",
-      " coefs[46]      0.28      0.27      0.28     -0.20      0.70    644.22      1.00\n",
-      " coefs[47]     -0.04      0.07     -0.04     -0.16      0.07    992.72      1.00\n",
-      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.03    734.82      1.00\n",
-      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.04   1801.99      1.00\n",
-      " coefs[50]     -0.85      0.59     -0.74     -1.69     -0.05   4857.12      1.00\n",
-      " coefs[51]     -0.08      0.17     -0.08     -0.38      0.17    656.17      1.00\n",
-      " coefs[52]     -0.06      0.16     -0.06     -0.34      0.17    660.34      1.00\n",
-      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.05    673.66      1.00\n",
-      " coefs[54]     -1.86      0.20     -1.84     -2.17     -1.51   4098.42      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 38 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      1.97      0.06      1.96      1.87      2.07  10096.48      1.00\n",
-      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12244.36      1.00\n",
-      "  coefs[2]     -0.04      0.06     -0.04     -0.15      0.07   4159.98      1.00\n",
-      "  coefs[3]     -0.33      0.03     -0.33     -0.38     -0.27   7749.88      1.00\n",
-      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8882.58      1.00\n",
-      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11482.48      1.00\n",
-      "  coefs[6]      0.07      0.24      0.06     -0.32      0.47   3120.93      1.00\n",
-      "  coefs[7]     -0.51      0.15     -0.51     -0.75     -0.26   3283.63      1.00\n",
-      "  coefs[8]      0.42      0.28      0.42     -0.05      0.87   3098.35      1.00\n",
-      "  coefs[9]     -0.06      0.03     -0.06     -0.11     -0.01  11951.39      1.00\n",
-      " coefs[10]      0.45      0.65      0.44     -0.62      1.53   3260.72      1.00\n",
-      " coefs[11]     -0.04      0.29     -0.05     -0.56      0.40   3274.76      1.00\n",
-      " coefs[12]      0.06      0.65      0.05     -1.00      1.15   3282.00      1.00\n",
-      " coefs[13]     -1.05      0.62     -1.00     -2.12     -0.12   5389.23      1.00\n",
-      " coefs[14]     -0.46      0.68     -0.35     -1.52      0.56   6658.42      1.00\n",
-      " coefs[15]     -0.79      0.56     -0.69     -1.65      0.05   5438.21      1.00\n",
-      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5338.59      1.00\n",
-      " coefs[17]     -0.27      0.23     -0.25     -0.63      0.11   1265.14      1.00\n",
-      " coefs[18]     -0.57      0.66     -0.46     -1.59      0.38   5781.56      1.00\n",
-      " coefs[19]     -0.46      0.68     -0.36     -1.53      0.61   6188.61      1.00\n",
-      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.04   5486.01      1.00\n",
-      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1964.40      1.00\n",
-      " coefs[22]      0.01      0.07      0.01     -0.11      0.13   1235.89      1.00\n",
-      " coefs[23]      0.10      0.25      0.10     -0.32      0.49    591.69      1.00\n",
-      " coefs[24]      0.08      0.16      0.08     -0.19      0.32    595.98      1.00\n",
-      " coefs[25]     -0.08      0.23     -0.08     -0.47      0.30    576.69      1.00\n",
-      " coefs[26]      0.03      0.18      0.03     -0.26      0.33    584.84      1.00\n",
-      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.14   5240.14      1.00\n",
-      " coefs[28]      0.03      1.00      0.03     -1.59      1.68  11781.73      1.00\n",
-      " coefs[29]      0.06      0.08      0.07     -0.06      0.19    634.64      1.00\n",
-      " coefs[30]      0.04      0.09      0.04     -0.12      0.18    665.09      1.00\n",
-      " coefs[31]     -0.76      0.58     -0.64     -1.62      0.05   4939.89      1.00\n",
-      " coefs[32]      0.04      0.09      0.04     -0.10      0.19    595.34      1.00\n",
-      " coefs[33]      0.15      0.13      0.15     -0.05      0.38    588.17      1.00\n",
-      " coefs[34]      0.91      0.59      0.79      0.10      1.77   4449.06      1.00\n",
-      " coefs[35]      0.29      0.24      0.30     -0.12      0.68    566.20      1.00\n",
-      " coefs[36]      0.35      0.31      0.35     -0.19      0.84    565.96      1.00\n",
-      " coefs[37]      0.19      0.20      0.19     -0.12      0.52    569.22      1.00\n",
-      " coefs[38]     -0.06      0.04     -0.05     -0.12      0.01    935.97      1.00\n",
-      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    737.66      1.00\n",
-      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    682.67      1.00\n",
-      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1363.24      1.00\n",
-      " coefs[42]      0.05      0.42      0.05     -0.64      0.72    564.74      1.00\n",
-      " coefs[43]      0.03      0.23      0.03     -0.38      0.39    570.94      1.00\n",
-      " coefs[44]      0.18      0.21      0.19     -0.18      0.53    568.55      1.00\n",
-      " coefs[45]      0.15      0.30      0.15     -0.35      0.63    562.05      1.00\n",
-      " coefs[46]      0.23      0.28      0.23     -0.24      0.68    565.69      1.00\n",
-      " coefs[47]     -0.84      0.57     -0.72     -1.69     -0.04   4863.24      1.00\n",
-      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    649.56      1.00\n",
-      " coefs[49]      0.03      1.01      0.02     -1.55      1.72  11743.21      1.00\n",
-      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   5084.52      1.00\n",
-      " coefs[51]     -0.09      0.17     -0.09     -0.38      0.18    574.15      1.00\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.41      0.12    576.37      1.00\n",
-      " coefs[53]     -0.18      0.13     -0.17     -0.39      0.03    578.29      1.00\n",
-      " coefs[54]     -1.71      0.19     -1.69     -2.00     -1.38   4122.53      1.00\n",
-      "\n",
-      "\n",
-      "\n",
-      " =============================== SUBPOSTERIOR 39 ===============================\n",
-      "\n",
-      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
-      "  coefs[0]      2.02      0.06      2.02      1.92      2.13  10022.35      1.00\n",
-      "  coefs[1]     -0.07      0.04     -0.07     -0.13     -0.02  11930.67      1.00\n",
-      "  coefs[2]      0.09      0.07      0.09     -0.03      0.21   3565.47      1.00\n",
-      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   7874.95      1.00\n",
-      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.04   8677.59      1.00\n",
-      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11143.46      1.00\n",
-      "  coefs[6]      0.64      0.30      0.63      0.17      1.14   2850.68      1.00\n",
-      "  coefs[7]     -0.90      0.18     -0.89     -1.21     -0.61   3006.07      1.00\n",
-      "  coefs[8]      1.05      0.35      1.04      0.50      1.63   2848.02      1.00\n",
-      "  coefs[9]      0.05      0.03      0.05      0.00      0.10  11434.28      1.00\n",
-      " coefs[10]      0.38      0.65      0.37     -0.73      1.41   3027.13      1.00\n",
-      " coefs[11]     -0.05      0.29     -0.05     -0.56      0.40   3049.82      1.00\n",
-      " coefs[12]      0.14      0.65      0.14     -0.93      1.20   3039.84      1.00\n",
-      " coefs[13]     -1.01      0.63     -0.94     -2.00     -0.00   4993.50      1.00\n",
-      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.53   5614.94      1.00\n",
-      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.06   4675.04      1.00\n",
-      " coefs[16]     -0.70      0.58     -0.59     -1.57      0.15   5153.50      1.00\n",
-      " coefs[17]     -0.05      0.17     -0.04     -0.32      0.23    652.24      1.01\n",
-      " coefs[18]     -0.52      0.66     -0.40     -1.52      0.44   6037.65      1.00\n",
-      " coefs[19]     -0.46      0.68     -0.36     -1.55      0.61   6114.54      1.00\n",
-      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.02   4987.38      1.00\n",
-      " coefs[21]     -0.75      0.59     -0.64     -1.59      0.05   4951.24      1.00\n",
-      " coefs[22]     -0.75      0.60     -0.63     -1.63      0.05   4435.53      1.00\n",
-      " coefs[23]      0.12      0.24      0.12     -0.27      0.51    500.82      1.01\n",
-      " coefs[24]      0.03      0.15      0.03     -0.24      0.26    526.83      1.01\n",
-      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.33    494.40      1.01\n",
-      " coefs[26]      0.01      0.17      0.01     -0.28      0.30    506.35      1.01\n",
-      " coefs[27]     -0.71      0.62     -0.59     -1.59      0.16   5403.79      1.00\n",
-      " coefs[28]      0.02      0.99      0.03     -1.55      1.70  10861.75      1.00\n",
-      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    543.44      1.01\n",
-      " coefs[30]      0.08      0.09      0.08     -0.06      0.22    601.06      1.01\n",
-      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13   1105.50      1.00\n",
-      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    526.65      1.01\n",
-      " coefs[33]      0.12      0.13      0.12     -0.10      0.32    494.20      1.01\n",
-      " coefs[34]      0.93      0.59      0.81      0.12      1.79   4585.26      1.00\n",
-      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    491.75      1.01\n",
-      " coefs[36]      0.37      0.30      0.37     -0.14      0.86    486.39      1.01\n",
-      " coefs[37]      0.15      0.19      0.15     -0.16      0.47    488.15      1.01\n",
-      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    676.92      1.01\n",
-      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    570.31      1.01\n",
-      " coefs[40]      0.02      0.05      0.03     -0.05      0.11    563.75      1.01\n",
-      " coefs[41]     -0.78      0.59     -0.66     -1.63      0.03   4822.95      1.00\n",
-      " coefs[42]      0.05      0.40      0.06     -0.59      0.74    487.94      1.01\n",
-      " coefs[43]      0.01      0.23      0.01     -0.36      0.38    491.71      1.01\n",
-      " coefs[44]      0.19      0.21      0.20     -0.17      0.52    491.92      1.01\n",
-      " coefs[45]      0.07      0.29      0.08     -0.42      0.53    489.32      1.01\n",
-      " coefs[46]      0.20      0.27      0.20     -0.26      0.63    486.73      1.01\n",
-      " coefs[47]     -0.10      0.07     -0.10     -0.21      0.01    773.52      1.01\n",
-      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.02    540.35      1.01\n",
-      " coefs[49]     -0.81      0.60     -0.69     -1.66     -0.02   4748.32      1.00\n",
-      " coefs[50]     -0.86      0.58     -0.74     -1.70     -0.08   4705.07      1.00\n",
-      " coefs[51]     -0.13      0.16     -0.13     -0.40      0.14    498.31      1.01\n",
-      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    504.10      1.01\n",
-      " coefs[53]     -0.15      0.13     -0.14     -0.35      0.06    502.86      1.01\n",
-      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   4340.91      1.00\n",
-      "\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "rngs = random.split(random.PRNGKey(1), K)\n",
-    "subposteriors = []\n",
-    "for i, (rng, shard) in enumerate(zip(rngs, shards)):\n",
-    "    sep = '=' * 31\n",
-    "    print('\\n ' + sep + ' SUBPOSTERIOR {:02d} '.format(i) + sep, end='')\n",
-    "    samples = get_subposterior(rng, shard, K)\n",
-    "    if not os.path.exists('.results'):\n",
-    "        os.makedir('.results')\n",
-    "    np.save('.results/subposterior_{:02d}.npy'.format(i), samples)\n",
-    "    subposteriors.append(samples)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### merge subposteriors"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "consensus_samples = consensus(subposteriors, 10000)\n",
-    "parametric_samples = parametric_draws(subposteriors, 10000)\n",
-    "np.save('.results/consensus_samples.npy', consensus_samples)\n",
-    "np.save('.results/parametric_samples.npy', parametric_samples)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### predict"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def predict(model, X, rng, sample):\n",
-    "    model = substitute(seed(model, rng), sample)\n",
-    "    model_trace = trace(model).get_trace(X, None)\n",
-    "    return model_trace['y']['value']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Consensus accuaracy: 0.771\n",
-      "Parametric accuaracy: 0.771\n"
-     ]
-    }
-   ],
-   "source": [
-    "rngs = random.split(random.PRNGKey(2), 10000)\n",
-    "\n",
-    "y_consensus = vmap(partial(predict, model, X_test))(rngs, consensus_samples)\n",
-    "y_consensus = (y_consensus.sum(axis=0) / y_consensus.shape[0]) >= 0.5\n",
-    "acc = (y_consensus == y_test).sum() / y_test.shape[0]\n",
-    "print('Consensus accuaracy: {}'.format(round(acc.item(), 4)))\n",
-    "\n",
-    "y_parametric = vmap(partial(predict, model, X_test))(rngs, parametric_samples)\n",
-    "y_parametric = (y_parametric.sum(axis=0) / y_parametric.shape[0]) >= 0.5\n",
-    "acc = (y_parametric == y_test).sum() / y_test.shape[0]\n",
-    "print('Parametric accuaracy: {}'.format(round(acc.item(), 4)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### train iaf"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from jax.experimental import stax"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "rng_guide, rng_init, rng_train = random.split(random.PRNGKey(3), 3)\n",
-    "opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
-    "guide = AutoIAFNormal(rng_guide, model, get_params, nonlinearity=stax.Elu,\n",
-    "                      skip_connections=False)\n",
-    "ll_scale = X_train.shape[0] // batch_size\n",
-    "svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params,\n",
-    "                              likelihood_scale=ll_scale)\n",
-    "batch_size = 1000\n",
-    "num_iters = ll_scale\n",
-    "\n",
-    "def epoch_train(epoch, opt_state, rng):\n",
-    "    # shuffle data\n",
-    "    rng, rng_shuffle = random.split(rng)\n",
-    "    idx = random.shuffle(rng_shuffle, np.arange(X_train.shape[0]))\n",
-    "    X = X_train[idx]\n",
-    "    y = y_train[idx]\n",
-    "    offset = epoch * num_iters\n",
-    "\n",
-    "    def body_fn(val, i):\n",
-    "        batch_X = lax.dynamic_slice_in_dim(X, i * batch_size, batch_size)\n",
-    "        batch_y = lax.dynamic_slice_in_dim(y, i * batch_size, batch_size)\n",
-    "        opt_state_, rng_ = val\n",
-    "        loss, opt_state_, rng_ = svi_update(offset + i, rng_, opt_state_,\n",
-    "                                            (batch_X, batch_y), (batch_X, batch_y))\n",
-    "        return (opt_state_, rng_), loss\n",
-    "\n",
-    "    (opt_state, _), losses = lax.scan(body_fn, (opt_state, rng), np.arange(num_iters))\n",
-    "    return opt_state, losses"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "opt_state, _ = svi_init(rng_init,\n",
-    "                        (X_train[:batch_size], y_train[:batch_size]),\n",
-    "                        (X_train[:batch_size], y_train[:batch_size]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Epoch 00 - loss 1883.5496 - acc 0.7612\n",
-      "Epoch 01 - loss 688.8702 - acc 0.7706\n",
-      "Epoch 02 - loss 617.3635 - acc 0.7685\n",
-      "Epoch 03 - loss 601.3757 - acc 0.7711\n",
-      "Epoch 04 - loss 598.3813 - acc 0.7687\n",
-      "Epoch 05 - loss 593.7759 - acc 0.7708\n",
-      "Epoch 06 - loss 593.0955 - acc 0.7692\n",
-      "Epoch 07 - loss 590.5724 - acc 0.7714\n",
-      "Epoch 08 - loss 589.2113 - acc 0.7693\n",
-      "Epoch 09 - loss 588.8226 - acc 0.7721\n"
-     ]
-    }
-   ],
-   "source": [
-    "losses = np.array([])\n",
-    "num_epochs = 10\n",
-    "rngs = random.split(random.PRNGKey(2), 10000)\n",
-    "for epoch in range(num_epochs):\n",
-    "    rng = random.fold_in(rng_train, epoch)\n",
-    "    opt_state, epoch_loss = epoch_train(epoch, opt_state, rng)\n",
-    "    iaf_samples = guide.sample_posterior(random.PRNGKey(4), opt_state, sample_shape=(10000,))\n",
-    "    y_iaf = vmap(partial(predict, model, X_test))(rngs, iaf_samples)\n",
-    "    y_iaf = (y_iaf.sum(axis=0) / y_iaf.shape[0]) >= 0.5\n",
-    "    acc = (y_iaf == y_test).sum() / y_test.shape[0]\n",
-    "    print(\"Epoch {:02d} - loss {:.4f} - acc {}\".format(\n",
-    "        epoch, np.mean(epoch_loss), round(acc.item(), 4)))\n",
-    "    losses = np.concatenate([losses, epoch_loss])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Epoch 00 - loss 254534.3438 - acc 0.6719\n",
-      "Epoch 01 - loss 65498.4805 - acc 0.6963\n",
-      "Epoch 02 - loss 58030.9766 - acc 0.6833\n",
-      "Epoch 03 - loss 11353.0801 - acc 0.697\n",
-      "Epoch 04 - loss 10766.7871 - acc 0.7035\n",
-      "Epoch 05 - loss 5903.0508 - acc 0.6917\n",
-      "Epoch 06 - loss 4735.4136 - acc 0.7204\n",
-      "Epoch 07 - loss 3767.8457 - acc 0.7249\n",
-      "Epoch 08 - loss 2702.3569 - acc 0.7115\n",
-      "Epoch 09 - loss 4246.7715 - acc 0.7243\n",
-      "Epoch 10 - loss 2887.8103 - acc 0.7419\n",
-      "Epoch 11 - loss 1575.2468 - acc 0.7423\n",
-      "Epoch 12 - loss 3265.4502 - acc 0.7482\n",
-      "Epoch 13 - loss 1635.4376 - acc 0.7575\n",
-      "Epoch 14 - loss 2030.9865 - acc 0.7576\n",
-      "Epoch 15 - loss 1211.5005 - acc 0.747\n",
-      "Epoch 16 - loss 1234.9969 - acc 0.7586\n",
-      "Epoch 17 - loss 1120.3951 - acc 0.7628\n",
-      "Epoch 18 - loss 1038.1304 - acc 0.7655\n",
-      "Epoch 19 - loss 1188.7095 - acc 0.7434\n",
-      "Epoch 20 - loss 1023.7824 - acc 0.7597\n",
-      "Epoch 21 - loss 1024.2365 - acc 0.7727\n",
-      "Epoch 22 - loss 1002.4470 - acc 0.759\n",
-      "Epoch 23 - loss 1038.4382 - acc 0.768\n",
-      "Epoch 24 - loss 940.9832 - acc 0.7611\n",
-      "Epoch 25 - loss 895.9312 - acc 0.7674\n",
-      "Epoch 26 - loss 1345.1897 - acc 0.7639\n",
-      "Epoch 27 - loss 917.5681 - acc 0.76\n",
-      "Epoch 28 - loss 934.0630 - acc 0.7578\n",
-      "Epoch 29 - loss 881.1840 - acc 0.7477\n",
-      "Epoch 30 - loss 945.5895 - acc 0.7615\n",
-      "Epoch 31 - loss 881.6766 - acc 0.7651\n",
-      "Epoch 32 - loss 856.6132 - acc 0.7531\n",
-      "Epoch 33 - loss 977.1152 - acc 0.7651\n",
-      "Epoch 34 - loss 860.5390 - acc 0.757\n",
-      "Epoch 35 - loss 860.3196 - acc 0.7687\n",
-      "Epoch 36 - loss 841.2369 - acc 0.7647\n",
-      "Epoch 37 - loss 851.6643 - acc 0.7592\n",
-      "Epoch 38 - loss 813.6900 - acc 0.7679\n",
-      "Epoch 39 - loss 812.2313 - acc 0.7544\n",
-      "Epoch 40 - loss 808.4932 - acc 0.7634\n",
-      "Epoch 41 - loss 886.4514 - acc 0.7698\n",
-      "Epoch 42 - loss 817.3934 - acc 0.7537\n",
-      "Epoch 43 - loss 789.4904 - acc 0.7707\n",
-      "Epoch 44 - loss 790.3774 - acc 0.7612\n",
-      "Epoch 45 - loss 770.7787 - acc 0.7664\n",
-      "Epoch 46 - loss 764.3374 - acc 0.7694\n",
-      "Epoch 47 - loss 742.7781 - acc 0.7739\n",
-      "Epoch 48 - loss 734.4012 - acc 0.7643\n",
-      "Epoch 49 - loss 725.6569 - acc 0.7688\n",
-      "Epoch 50 - loss 713.1312 - acc 0.7696\n",
-      "Epoch 51 - loss 702.3688 - acc 0.7701\n",
-      "Epoch 52 - loss 694.8310 - acc 0.768\n",
-      "Epoch 53 - loss 690.0838 - acc 0.7679\n",
-      "Epoch 54 - loss 680.3116 - acc 0.7689\n",
-      "Epoch 55 - loss 688.9963 - acc 0.7622\n",
-      "Epoch 56 - loss 671.6235 - acc 0.7716\n",
-      "Epoch 57 - loss 661.0634 - acc 0.7642\n",
-      "Epoch 58 - loss 654.5287 - acc 0.7706\n",
-      "Epoch 59 - loss 719.4338 - acc 0.7696\n",
-      "Epoch 60 - loss 667.0007 - acc 0.7694\n",
-      "Epoch 61 - loss 649.3066 - acc 0.7701\n",
-      "Epoch 62 - loss 639.6379 - acc 0.7712\n",
-      "Epoch 63 - loss 634.2900 - acc 0.7695\n",
-      "Epoch 64 - loss 630.7141 - acc 0.7666\n",
-      "Epoch 65 - loss 628.7311 - acc 0.7717\n",
-      "Epoch 66 - loss 622.4650 - acc 0.7671\n",
-      "Epoch 67 - loss 619.6395 - acc 0.7696\n",
-      "Epoch 68 - loss 618.3934 - acc 0.7711\n",
-      "Epoch 69 - loss 613.0114 - acc 0.7702\n",
-      "Epoch 70 - loss 613.1573 - acc 0.7714\n",
-      "Epoch 71 - loss 608.6863 - acc 0.7656\n",
-      "Epoch 72 - loss 603.2803 - acc 0.7718\n",
-      "Epoch 73 - loss 604.5390 - acc 0.7671\n",
-      "Epoch 74 - loss 599.7892 - acc 0.7716\n",
-      "Epoch 75 - loss 598.3097 - acc 0.7695\n",
-      "Epoch 76 - loss 597.3398 - acc 0.77\n",
-      "Epoch 77 - loss 592.6534 - acc 0.7698\n",
-      "Epoch 78 - loss 590.7097 - acc 0.7686\n",
-      "Epoch 79 - loss 590.5514 - acc 0.7692\n",
-      "Epoch 80 - loss 588.7484 - acc 0.7694\n",
-      "Epoch 81 - loss 589.0543 - acc 0.7723\n",
-      "Epoch 82 - loss 586.3735 - acc 0.7697\n",
-      "Epoch 83 - loss 589.2031 - acc 0.7659\n",
-      "Epoch 84 - loss 587.5204 - acc 0.7697\n",
-      "Epoch 85 - loss 586.9933 - acc 0.7679\n",
-      "Epoch 86 - loss 586.1766 - acc 0.7689\n",
-      "Epoch 87 - loss 584.0955 - acc 0.7702\n",
-      "Epoch 88 - loss 584.7559 - acc 0.7699\n",
-      "Epoch 89 - loss 583.4180 - acc 0.7715\n",
-      "Epoch 90 - loss 583.9426 - acc 0.7715\n",
-      "Epoch 91 - loss 582.8043 - acc 0.7687\n",
-      "Epoch 92 - loss 582.0665 - acc 0.7677\n",
-      "Epoch 93 - loss 582.5842 - acc 0.7703\n",
-      "Epoch 94 - loss 583.2501 - acc 0.7711\n",
-      "Epoch 95 - loss 582.0706 - acc 0.7708\n",
-      "Epoch 96 - loss 581.0920 - acc 0.77\n",
-      "Epoch 97 - loss 581.4358 - acc 0.7716\n",
-      "Epoch 98 - loss 582.6833 - acc 0.7713\n",
-      "Epoch 99 - loss 581.7660 - acc 0.7716\n"
-     ]
-    }
-   ],
-   "source": [
-    "losses = np.array([])\n",
-    "num_epochs = 100\n",
-    "rngs = random.split(random.PRNGKey(2), 10000)\n",
-    "for epoch in range(num_epochs):\n",
-    "    rng = random.fold_in(rng_train, epoch)\n",
-    "    opt_state, epoch_loss = epoch_train(epoch, opt_state, rng)\n",
-    "    iaf_samples = guide.sample_posterior(random.PRNGKey(4), opt_state, sample_shape=(10000,))\n",
-    "    y_iaf = vmap(partial(predict, model, X_test))(rngs, iaf_samples)\n",
-    "    y_iaf = (y_iaf.sum(axis=0) / y_iaf.shape[0]) >= 0.5\n",
-    "    acc = (y_iaf == y_test).sum() / y_test.shape[0]\n",
-    "    print(\"Epoch {:02d} - loss {:.4f} - acc {}\".format(\n",
-    "        epoch, np.mean(epoch_loss), round(acc.item(), 4)))\n",
-    "    losses = np.concatenate([losses, epoch_loss])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Flow HMC"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "transform = guide.get_transform(opt_state)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "unpack_fn = guide.unpack_latent"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def make_transformed_pe(potential_fn, transform, unpack_fn):\n",
-    "    def transformed_potential_fn(z):\n",
-    "        u, intermediates = transform.call_with_intermediates(z)\n",
-    "        logdet = transform.log_abs_det_jacobian(z, u, intermediates=intermediates)\n",
-    "        return potential_fn(unpack_fn(u)) + logdet\n",
-    "\n",
-    "    return transformed_potential_fn"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python (pydata)",
-   "language": "python",
-   "name": "pydata"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}

From e491230630e1d3e80c499095d811d644de5f2d15 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Sun, 11 Aug 2019 02:52:44 -0400
Subject: [PATCH 23/35] add flowhmc section, currently do not work

---
 notebooks/source/covtype.ipynb | 3114 ++++++++++++++++++++++++++++++++
 1 file changed, 3114 insertions(+)
 create mode 100644 notebooks/source/covtype.ipynb

diff --git a/notebooks/source/covtype.ipynb b/notebooks/source/covtype.ipynb
new file mode 100644
index 000000000..47deb534b
--- /dev/null
+++ b/notebooks/source/covtype.ipynb
@@ -0,0 +1,3114 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from functools import partial\n",
+    "import os; os.environ['XLA_FLAGS'] = '--xla_force_host_platform_device_count=4'\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as onp\n",
+    "\n",
+    "from jax import jit, lax, random, vmap\n",
+    "from jax.config import config; config.update('jax_platform_name', 'cpu')\n",
+    "from jax.experimental import optimizers, stax\n",
+    "import jax.numpy as np\n",
+    "\n",
+    "from numpyro.contrib.autoguide import AutoIAFNormal\n",
+    "import numpyro.distributions as dist\n",
+    "from numpyro.examples.datasets import COVTYPE, load_dataset\n",
+    "from numpyro.handlers import sample, scale, seed, substitute, trace\n",
+    "from numpyro.hmc_util import consensus, initialize_model, parametric_draws\n",
+    "from numpyro.mcmc import mcmc\n",
+    "from numpyro.svi import elbo, svi"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### load data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Data shape: (581012, 55)\n",
+      "Label distribution: 211840 has label 1, 369172 has label 0\n"
+     ]
+    }
+   ],
+   "source": [
+    "def _load_dataset():\n",
+    "    _, fetch = load_dataset(COVTYPE, shuffle=False)\n",
+    "    features, labels = fetch()\n",
+    "\n",
+    "    # normalize features and add intercept\n",
+    "    features = (features - features.mean(0)) / features.std(0)\n",
+    "    features = np.hstack([features, np.ones((features.shape[0], 1))])\n",
+    "\n",
+    "    # make binary feature\n",
+    "    _, counts = onp.unique(labels, return_counts=True)\n",
+    "    specific_category = np.argmax(counts)\n",
+    "    labels = (labels == specific_category)\n",
+    "\n",
+    "    N, dim = features.shape\n",
+    "    print(\"Data shape:\", features.shape)\n",
+    "    print(\"Label distribution: {} has label 1, {} has label 0\"\n",
+    "          .format(labels.sum(), N - labels.sum()))\n",
+    "    return features, labels\n",
+    "\n",
+    "X_full, y_full = _load_dataset()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### prepare train shards and test set"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Train set contains 400000 (68.85%) data points.\n",
+      "Test set contains 181012 (31.15%) data points.\n"
+     ]
+    }
+   ],
+   "source": [
+    "def get_train_shards_and_test_data(X, y, K, N, rng=None):\n",
+    "    if rng is not None:\n",
+    "        idxs = random.shuffle(rng, np.arange(X.shape[0]))\n",
+    "        X = X[idxs]\n",
+    "        y = y[idxs]\n",
+    "    shards = []\n",
+    "    for i in range(K):\n",
+    "        shards.append((X[i * N: (i + 1) * N], y[i * N: (i + 1) * N]))\n",
+    "    train_data = (X[:K * N], y[:K * N])\n",
+    "    test_data = (X[K * N:], y[K * N:])\n",
+    "    return shards, train_data, test_data\n",
+    "\n",
+    "K, N = 40, 10000\n",
+    "shards, (X_train, y_train), (X_test, y_test) = get_train_shards_and_test_data(\n",
+    "    X_full, y_full, K, N, random.PRNGKey(0))\n",
+    "print(\"Train set contains {} ({}%) data points.\".format(\n",
+    "    K * N, round(K * N / X_full.shape[0] * 100, 2)))\n",
+    "print(\"Test set contains {} ({}%) data points.\".format(\n",
+    "    X_full.shape[0] - K * N, round(100 - K * N / X_full.shape[0] * 100, 2)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def model(X, y, prior_scale=1, likelihood_scale=1):\n",
+    "    with scale(prior_scale):\n",
+    "        coefs = sample('coefs', dist.Normal(np.zeros(X.shape[-1]), np.ones(X.shape[-1])))\n",
+    "    with scale(likelihood_scale):\n",
+    "        return sample('y', dist.Bernoulli(logits=np.dot(X, coefs)), obs=y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### sampling"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_subposterior(rng, shard, K):\n",
+    "    rngs = random.split(rng, 4)\n",
+    "    X, y = shard\n",
+    "    init_params, potential_fn, _ = initialize_model(rngs, model, X, y, prior_scale=1 / K)\n",
+    "    samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
+    "                   num_chains=4, potential_fn=potential_fn)\n",
+    "    return samples"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      " =============================== SUBPOSTERIOR 00 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.94      0.06      1.94      1.84      2.04  10596.19      1.00\n",
+      "  coefs[1]      0.00      0.03      0.00     -0.06      0.06  13018.15      1.00\n",
+      "  coefs[2]     -0.05      0.07     -0.05     -0.15      0.06   3962.76      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   8349.60      1.00\n",
+      "  coefs[4]     -0.13      0.04     -0.13     -0.19     -0.07   9673.05      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.15     -0.04  11774.95      1.00\n",
+      "  coefs[6]      0.33      0.25      0.32     -0.08      0.73   3044.25      1.00\n",
+      "  coefs[7]     -0.70      0.15     -0.69     -0.94     -0.45   3230.34      1.00\n",
+      "  coefs[8]      0.61      0.29      0.60      0.12      1.08   3048.04      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.01  11912.89      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.66      1.50   3045.41      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.42   3041.88      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.99      1.17   3040.15      1.00\n",
+      " coefs[13]     -0.94      0.65     -0.88     -2.00      0.08   5089.97      1.00\n",
+      " coefs[14]     -0.48      0.67     -0.37     -1.51      0.56   5935.95      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.69     -1.65      0.03   5174.92      1.00\n",
+      " coefs[16]     -0.71      0.60     -0.59     -1.63      0.11   4779.67      1.00\n",
+      " coefs[17]     -0.28      0.22     -0.27     -0.65      0.08   1027.92      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.46     -1.58      0.40   5873.46      1.00\n",
+      " coefs[19]     -0.49      0.67     -0.39     -1.61      0.53   5699.48      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.03   5339.04      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1357.53      1.00\n",
+      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11   1117.18      1.00\n",
+      " coefs[23]     -0.07      0.25     -0.07     -0.47      0.34    537.29      1.00\n",
+      " coefs[24]     -0.04      0.16     -0.04     -0.31      0.21    542.14      1.00\n",
+      " coefs[25]     -0.01      0.23     -0.02     -0.39      0.35    498.36      1.00\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.31      0.27    506.74      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.12   5016.54      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.71  11735.13      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.04      0.21    522.46      1.00\n",
+      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    581.10      1.00\n",
+      " coefs[31]      0.04      0.08      0.04     -0.09      0.16    822.05      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.03      0.26    518.96      1.00\n",
+      " coefs[33]      0.13      0.13      0.13     -0.08      0.34    494.96      1.00\n",
+      " coefs[34]      0.06      0.05      0.06     -0.02      0.15    858.21      1.00\n",
+      " coefs[35]      0.38      0.24      0.38     -0.01      0.77    488.03      1.00\n",
+      " coefs[36]      0.40      0.31      0.40     -0.10      0.90    484.06      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.13      0.50    491.13      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05    833.97      1.00\n",
+      " coefs[39]     -0.01      0.08     -0.01     -0.14      0.11    601.79      1.00\n",
+      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    632.43      1.00\n",
+      " coefs[41]     -0.77      0.58     -0.65     -1.62      0.05   5172.22      1.00\n",
+      " coefs[42]      0.11      0.41      0.11     -0.56      0.77    485.90      1.00\n",
+      " coefs[43]     -0.04      0.23     -0.04     -0.40      0.34    487.10      1.00\n",
+      " coefs[44]      0.16      0.21      0.16     -0.19      0.50    486.21      1.00\n",
+      " coefs[45]      0.12      0.30      0.12     -0.36      0.61    485.58      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.26      0.64    488.71      1.00\n",
+      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    688.12      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    530.56      1.00\n",
+      " coefs[49]      0.02      1.00      0.01     -1.59      1.68  11841.74      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4715.49      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.17    496.97      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    491.79      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    498.09      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4068.47      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 01 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.03      0.06      2.03      1.93      2.13   6297.01      1.00\n",
+      "  coefs[1]     -0.10      0.03     -0.10     -0.16     -0.05   6696.79      1.00\n",
+      "  coefs[2]     -0.04      0.07     -0.04     -0.16      0.09   2407.61      1.00\n",
+      "  coefs[3]     -0.23      0.03     -0.24     -0.29     -0.18   5620.77      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   5804.19      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13   6953.33      1.00\n",
+      "  coefs[6]      0.23      0.30      0.23     -0.26      0.72   2060.03      1.00\n",
+      "  coefs[7]     -0.64      0.18     -0.64     -0.94     -0.34   2165.40      1.00\n",
+      "  coefs[8]      0.68      0.35      0.67      0.11      1.27   2051.67      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.02   7364.88      1.00\n",
+      " coefs[10]      0.42      0.65      0.42     -0.69      1.45   2455.62      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.05     -0.54      0.41   2496.49      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -1.06      1.08   2474.35      1.00\n",
+      " coefs[13]     -1.02      0.64     -0.97     -2.04      0.02   3633.72      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.36     -1.51      0.55   3974.22      1.00\n",
+      " coefs[15]     -0.78      0.56     -0.68     -1.61      0.05   3326.03      1.00\n",
+      " coefs[16]     -0.74      0.58     -0.63     -1.61      0.10   3931.39      1.00\n",
+      " coefs[17]     -0.11      0.18     -0.10     -0.41      0.20    716.27      1.01\n",
+      " coefs[18]     -0.54      0.67     -0.44     -1.55      0.44   4309.01      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.35     -1.56      0.59   4171.46      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   3801.33      1.00\n",
+      " coefs[21]      0.03      0.03      0.03     -0.01      0.07    928.09      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    821.22      1.01\n",
+      " coefs[23]      0.03      0.24      0.04     -0.38      0.40    486.42      1.01\n",
+      " coefs[24]      0.05      0.15      0.05     -0.20      0.29    508.69      1.01\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.43      0.31    474.61      1.01\n",
+      " coefs[26]      0.01      0.18      0.02     -0.27      0.31    482.02      1.01\n",
+      " coefs[27]     -0.68      0.63     -0.56     -1.60      0.18   3544.17      1.00\n",
+      " coefs[28]     -0.78      0.60     -0.66     -1.60      0.03   3720.32      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.03      0.21    525.53      1.01\n",
+      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    779.43      1.01\n",
+      " coefs[31]     -0.04      0.10     -0.03     -0.19      0.11   1169.81      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    512.40      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.37    482.55      1.01\n",
+      " coefs[34]      0.93      0.59      0.82      0.11      1.79   3574.15      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    473.55      1.01\n",
+      " coefs[36]      0.30      0.30      0.30     -0.21      0.78    470.35      1.01\n",
+      " coefs[37]      0.17      0.19      0.17     -0.16      0.47    467.05      1.01\n",
+      " coefs[38]     -0.04      0.04     -0.04     -0.11      0.02    769.86      1.01\n",
+      " coefs[39]      0.01      0.08      0.01     -0.11      0.14    578.20      1.01\n",
+      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.08    612.50      1.01\n",
+      " coefs[41]     -0.80      0.59     -0.67     -1.64      0.04   3531.23      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.64      0.68    469.07      1.01\n",
+      " coefs[43]      0.02      0.23      0.02     -0.35      0.39    472.51      1.01\n",
+      " coefs[44]      0.16      0.21      0.16     -0.19      0.49    471.76      1.01\n",
+      " coefs[45]      0.09      0.29      0.09     -0.40      0.55    469.03      1.01\n",
+      " coefs[46]      0.23      0.27      0.23     -0.22      0.67    471.88      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.04    839.36      1.01\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    510.68      1.01\n",
+      " coefs[49]      0.03      1.01      0.03     -1.59      1.76   7599.21      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.67     -0.07   3259.83      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.12    472.94      1.01\n",
+      " coefs[52]     -0.15      0.16     -0.15     -0.40      0.11    473.82      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.03    488.46      1.01\n",
+      " coefs[54]     -1.64      0.18     -1.63     -1.94     -1.34   2819.50      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 02 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.07  10141.39      1.00\n",
+      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.01  11681.33      1.00\n",
+      "  coefs[2]      0.05      0.08      0.05     -0.08      0.18   3349.04      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.22   8028.85      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.06   9352.06      1.00\n",
+      "  coefs[5]     -0.13      0.03     -0.13     -0.18     -0.07  11348.87      1.00\n",
+      "  coefs[6]      0.80      0.32      0.80      0.28      1.32   2779.37      1.00\n",
+      "  coefs[7]     -1.06      0.19     -1.06     -1.37     -0.74   2899.08      1.00\n",
+      "  coefs[8]      1.32      0.37      1.32      0.71      1.93   2786.07      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  12106.53      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.64      1.50   2853.02      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.39   2876.41      1.00\n",
+      " coefs[12]      0.13      0.65      0.13     -0.96      1.18   2851.32      1.00\n",
+      " coefs[13]     -1.08      0.62     -1.02     -2.08     -0.10   4547.27      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.56   5752.40      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.06   4399.13      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.58      0.16   5696.39      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.13     -0.44      0.18    742.08      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.58      0.39   5940.96      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.35     -1.54      0.62   5852.71      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5257.50      1.00\n",
+      " coefs[21]     -0.76      0.58     -0.64     -1.60      0.03   5145.51      1.00\n",
+      " coefs[22]      0.03      0.08      0.03     -0.08      0.16   1171.01      1.00\n",
+      " coefs[23]      0.16      0.25      0.15     -0.26      0.57    534.48      1.00\n",
+      " coefs[24]      0.02      0.16      0.02     -0.25      0.28    535.89      1.00\n",
+      " coefs[25]     -0.15      0.24     -0.16     -0.56      0.23    527.60      1.00\n",
+      " coefs[26]      0.06      0.18      0.06     -0.25      0.36    526.14      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.61      0.13   5205.52      1.00\n",
+      " coefs[28]      0.03      1.00      0.04     -1.61      1.65  10712.86      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    607.37      1.00\n",
+      " coefs[30]     -0.00      0.10     -0.00     -0.16      0.15    652.04      1.00\n",
+      " coefs[31]     -0.02      0.10     -0.01     -0.17      0.13   1134.64      1.00\n",
+      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    535.91      1.00\n",
+      " coefs[33]      0.15      0.14      0.15     -0.08      0.36    527.35      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4974.60      1.00\n",
+      " coefs[35]      0.38      0.25      0.38     -0.04      0.78    520.29      1.00\n",
+      " coefs[36]      0.37      0.32      0.37     -0.14      0.92    516.69      1.00\n",
+      " coefs[37]      0.18      0.20      0.17     -0.17      0.49    518.95      1.00\n",
+      " coefs[38]     -0.80      0.58     -0.68     -1.65     -0.01   5323.77      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    622.80      1.00\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    571.08      1.01\n",
+      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1236.93      1.00\n",
+      " coefs[42]      0.07      0.43      0.07     -0.61      0.79    513.79      1.00\n",
+      " coefs[43]      0.01      0.24      0.01     -0.38      0.41    521.37      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.21      0.52    511.80      1.00\n",
+      " coefs[45]      0.08      0.31      0.08     -0.43      0.58    514.38      1.00\n",
+      " coefs[46]      0.23      0.29      0.23     -0.23      0.71    515.12      1.00\n",
+      " coefs[47]     -0.13      0.09     -0.13     -0.27      0.01   1051.75      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    574.66      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.63      0.02   5085.05      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.07   4703.61      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.17    522.50      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.07     -0.34      0.20    518.37      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    526.44      1.00\n",
+      " coefs[54]     -1.67      0.19     -1.65     -1.95     -1.36   3894.03      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 03 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9308.68      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.04  11831.11      1.00\n",
+      "  coefs[2]     -0.08      0.06     -0.08     -0.18      0.03   3625.92      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.33     -0.22   7283.21      1.00\n",
+      "  coefs[4]     -0.09      0.03     -0.09     -0.14     -0.03   8157.44      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10004.68      1.00\n",
+      "  coefs[6]      0.04      0.24      0.04     -0.35      0.44   2665.26      1.00\n",
+      "  coefs[7]     -0.57      0.15     -0.57     -0.80     -0.31   2781.87      1.00\n",
+      "  coefs[8]      0.33      0.28      0.33     -0.12      0.80   2642.32      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11808.21      1.00\n",
+      " coefs[10]      0.37      0.65      0.37     -0.72      1.45   2985.63      1.00\n",
+      " coefs[11]     -0.00      0.29     -0.01     -0.48      0.49   2998.92      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2991.93      1.00\n",
+      " coefs[13]     -0.99      0.63     -0.92     -1.99      0.04   4876.03      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.53      0.50   5544.85      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.06   4454.60      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.60     -1.61      0.13   4989.00      1.00\n",
+      " coefs[17]      0.05      0.17      0.05     -0.23      0.32    633.85      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.54      0.43   5998.03      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.52      0.63   5489.12      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.61      0.02   5007.75      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1821.60      1.00\n",
+      " coefs[22]     -0.00      0.08      0.00     -0.13      0.11   1044.03      1.00\n",
+      " coefs[23]      0.02      0.26      0.02     -0.40      0.45    600.96      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.24      0.30    591.14      1.00\n",
+      " coefs[25]     -0.05      0.24     -0.05     -0.45      0.34    569.65      1.00\n",
+      " coefs[26]     -0.00      0.19     -0.00     -0.29      0.33    572.75      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   4787.94      1.00\n",
+      " coefs[28]      0.03      0.99      0.04     -1.57      1.67   9415.44      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.21    615.59      1.00\n",
+      " coefs[30]      0.03      0.10      0.03     -0.13      0.19    749.84      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.11      0.15    937.97      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    585.50      1.00\n",
+      " coefs[33]      0.14      0.14      0.14     -0.08      0.37    578.11      1.00\n",
+      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1184.94      1.00\n",
+      " coefs[35]      0.34      0.25      0.34     -0.08      0.75    562.89      1.00\n",
+      " coefs[36]      0.36      0.32      0.36     -0.15      0.92    562.32      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.51    564.23      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.10      0.03    914.20      1.00\n",
+      " coefs[39]     -0.83      0.57     -0.71     -1.68     -0.05   4856.42      1.00\n",
+      " coefs[40]      0.09      0.05      0.09     -0.00      0.17    716.14      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.66     -1.62      0.04   5147.75      1.00\n",
+      " coefs[42]      0.06      0.43      0.06     -0.63      0.80    560.74      1.00\n",
+      " coefs[43]      0.04      0.24      0.04     -0.36      0.44    567.24      1.00\n",
+      " coefs[44]      0.23      0.22      0.23     -0.14      0.59    562.82      1.00\n",
+      " coefs[45]      0.13      0.31      0.13     -0.38      0.65    562.89      1.00\n",
+      " coefs[46]      0.21      0.29      0.21     -0.26      0.69    560.89      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.07    884.93      1.00\n",
+      " coefs[48]     -0.01      0.07     -0.01     -0.11      0.11    642.70      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.66      0.01   4636.00      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.72     -1.68     -0.06   4578.95      1.00\n",
+      " coefs[51]     -0.07      0.18     -0.07     -0.36      0.22    573.25      1.00\n",
+      " coefs[52]     -0.11      0.17     -0.11     -0.39      0.15    567.32      1.00\n",
+      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.04    584.89      1.00\n",
+      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.43   3787.09      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 04 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9663.05      1.00\n",
+      "  coefs[1]      0.01      0.03      0.01     -0.04      0.07  12229.09      1.00\n",
+      "  coefs[2]     -0.05      0.08     -0.05     -0.18      0.08   3518.69      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.26     -0.32     -0.21   7811.88      1.00\n",
+      "  coefs[4]     -0.14      0.03     -0.14     -0.20     -0.09   8939.99      1.00\n",
+      "  coefs[5]     -0.21      0.03     -0.21     -0.26     -0.15  10756.10      1.00\n",
+      "  coefs[6]      0.29      0.32      0.28     -0.22      0.82   2819.50      1.00\n",
+      "  coefs[7]     -0.72      0.19     -0.72     -1.04     -0.41   2925.77      1.00\n",
+      "  coefs[8]      0.69      0.37      0.69      0.08      1.29   2825.15      1.00\n",
+      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  12007.14      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.67      1.47   3220.08      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3229.13      1.00\n",
+      " coefs[12]      0.10      0.65      0.09     -1.05      1.08   3214.88      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.99     -2.05     -0.06   5156.93      1.00\n",
+      " coefs[14]     -0.45      0.68     -0.35     -1.52      0.56   5786.49      1.00\n",
+      " coefs[15]     -0.76      0.58     -0.65     -1.65      0.08   4260.86      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.60      0.12   5213.66      1.00\n",
+      " coefs[17]     -0.04      0.17     -0.04     -0.31      0.23    558.39      1.00\n",
+      " coefs[18]     -0.52      0.68     -0.40     -1.59      0.44   6109.99      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.38     -1.58      0.58   5597.20      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5070.21      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.63      0.01   4634.14      1.00\n",
+      " coefs[22]      0.10      0.06      0.10      0.01      0.19    642.58      1.00\n",
+      " coefs[23]      0.12      0.24      0.11     -0.29      0.51    465.45      1.00\n",
+      " coefs[24]      0.09      0.15      0.09     -0.15      0.35    470.90      1.00\n",
+      " coefs[25]     -0.11      0.23     -0.11     -0.48      0.27    454.80      1.00\n",
+      " coefs[26]      0.00      0.18      0.00     -0.30      0.29    466.84      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.60      0.14   5204.11      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.60      1.66  11259.68      1.00\n",
+      " coefs[29]      0.09      0.08      0.08     -0.03      0.22    488.93      1.00\n",
+      " coefs[30]      0.02      0.09      0.03     -0.13      0.18    610.00      1.00\n",
+      " coefs[31]     -0.75      0.59     -0.63     -1.60      0.08   4911.00      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.05      0.23    463.51      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.06      0.37    460.50      1.00\n",
+      " coefs[34]      0.93      0.59      0.80      0.12      1.77   4713.75      1.00\n",
+      " coefs[35]      0.32      0.24      0.32     -0.07      0.72    450.32      1.00\n",
+      " coefs[36]      0.32      0.31      0.32     -0.19      0.82    446.76      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    449.21      1.00\n",
+      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.02   1126.07      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    542.39      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.12    514.96      1.00\n",
+      " coefs[41]     -0.01      0.07     -0.01     -0.12      0.10   1089.97      1.00\n",
+      " coefs[42]      0.05      0.41      0.05     -0.65      0.69    447.89      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.36      0.39    451.39      1.00\n",
+      " coefs[44]      0.18      0.21      0.18     -0.16      0.53    448.32      1.00\n",
+      " coefs[45]      0.12      0.30      0.12     -0.36      0.60    447.13      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.23      0.67    449.59      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.11     -0.25      0.03    961.34      1.00\n",
+      " coefs[48]     -0.10      0.06     -0.10     -0.20      0.00    482.43      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1292.54      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.73     -1.68     -0.06   5019.30      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.09     -0.36      0.19    453.50      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.14    453.09      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.37      0.05    458.05      1.00\n",
+      " coefs[54]     -1.69      0.19     -1.68     -2.00     -1.40   4062.23      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 05 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.98      0.06      1.98      1.88      2.08  10055.48      1.00\n",
+      "  coefs[1]     -0.09      0.03     -0.09     -0.15     -0.03  13343.50      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.06   3771.35      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.20   8377.00      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   9458.58      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  11099.64      1.00\n",
+      "  coefs[6]      0.16      0.28      0.16     -0.28      0.65   2986.01      1.00\n",
+      "  coefs[7]     -0.68      0.17     -0.67     -0.95     -0.39   3098.70      1.00\n",
+      "  coefs[8]      0.53      0.33      0.53      0.01      1.08   2974.13      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  12492.35      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.63      1.52   3281.51      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.05     -0.53      0.44   3280.68      1.00\n",
+      " coefs[12]      0.09      0.65      0.08     -0.95      1.20   3275.10      1.00\n",
+      " coefs[13]     -1.02      0.62     -0.96     -1.99      0.03   5048.16      1.00\n",
+      " coefs[14]     -0.45      0.66     -0.34     -1.48      0.55   6484.69      1.00\n",
+      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.07   4874.24      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.59     -1.60      0.13   5196.60      1.00\n",
+      " coefs[17]     -0.85      0.54     -0.75     -1.71     -0.04   4288.80      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.42   5984.25      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.52      0.61   6184.44      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.61      0.02   5183.95      1.00\n",
+      " coefs[21]     -0.76      0.60     -0.65     -1.61      0.06   5107.29      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.14    931.40      1.00\n",
+      " coefs[23]      0.12      0.25      0.12     -0.29      0.53    654.15      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    661.51      1.00\n",
+      " coefs[25]      0.02      0.24      0.02     -0.38      0.39    640.94      1.00\n",
+      " coefs[26]      0.08      0.18      0.08     -0.22      0.38    650.77      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   5054.07      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.60      1.71  12236.32      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    716.26      1.00\n",
+      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    819.35      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.63     -1.63      0.05   5197.70      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    664.44      1.00\n",
+      " coefs[33]      0.15      0.13      0.16     -0.07      0.37    636.44      1.00\n",
+      " coefs[34]      0.08      0.05      0.08      0.00      0.16    913.04      1.00\n",
+      " coefs[35]      0.38      0.25      0.38     -0.04      0.76    631.09      1.00\n",
+      " coefs[36]      0.41      0.32      0.42     -0.11      0.91    625.04      1.00\n",
+      " coefs[37]      0.16      0.20      0.17     -0.17      0.47    634.99      1.00\n",
+      " coefs[38]     -0.01      0.05     -0.01     -0.10      0.07   1734.43      1.00\n",
+      " coefs[39]      0.06      0.08      0.06     -0.07      0.18    733.19      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    751.19      1.00\n",
+      " coefs[41]     -0.77      0.58     -0.64     -1.64      0.04   5405.80      1.00\n",
+      " coefs[42]      0.13      0.42      0.13     -0.55      0.82    630.46      1.00\n",
+      " coefs[43]      0.06      0.24      0.07     -0.32      0.44    631.90      1.00\n",
+      " coefs[44]      0.19      0.22      0.19     -0.18      0.53    624.94      1.00\n",
+      " coefs[45]      0.17      0.30      0.17     -0.33      0.65    625.77      1.00\n",
+      " coefs[46]      0.25      0.28      0.25     -0.22      0.70    622.20      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.12     -0.25      0.03   1352.86      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    690.67      1.00\n",
+      " coefs[49]      0.01      0.03      0.01     -0.04      0.06   2201.81      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.07   4536.52      1.00\n",
+      " coefs[51]     -0.07      0.17     -0.07     -0.36      0.19    638.33      1.00\n",
+      " coefs[52]     -0.06      0.16     -0.05     -0.32      0.21    633.89      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.08    644.18      1.00\n",
+      " coefs[54]     -1.83      0.20     -1.82     -2.15     -1.50   4430.47      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 06 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.95      0.06      1.95      1.85      2.05  10029.37      1.00\n",
+      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02  12149.78      1.00\n",
+      "  coefs[2]     -0.07      0.07     -0.07     -0.18      0.04   3538.75      1.00\n",
+      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.23   7831.87      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.13     -0.02   8546.42      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  11509.36      1.00\n",
+      "  coefs[6]      0.22      0.26      0.21     -0.20      0.65   2659.06      1.00\n",
+      "  coefs[7]     -0.68      0.16     -0.68     -0.94     -0.42   2786.69      1.00\n",
+      "  coefs[8]      0.62      0.30      0.61      0.14      1.13   2692.12      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12142.73      1.00\n",
+      " coefs[10]      0.44      0.66      0.43     -0.66      1.52   3204.45      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.53      0.44   3207.91      1.00\n",
+      " coefs[12]      0.10      0.66      0.10     -1.00      1.17   3206.53      1.00\n",
+      " coefs[13]     -1.07      0.62     -1.02     -2.08     -0.09   4936.60      1.00\n",
+      " coefs[14]     -0.47      0.68     -0.35     -1.47      0.58   5590.17      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.63      0.08   4904.63      1.00\n",
+      " coefs[16]     -0.73      0.57     -0.62     -1.60      0.10   5217.49      1.00\n",
+      " coefs[17]      0.01      0.16      0.01     -0.25      0.27    685.60      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.55      0.43   5794.67      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.55      0.59   5598.62      1.00\n",
+      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4899.15      1.00\n",
+      " coefs[21]     -0.79      0.59     -0.66     -1.64      0.01   4949.36      1.00\n",
+      " coefs[22]      0.05      0.05      0.05     -0.04      0.14    761.87      1.00\n",
+      " coefs[23]      0.13      0.24      0.13     -0.25      0.54    591.47      1.00\n",
+      " coefs[24]      0.13      0.15      0.13     -0.11      0.38    583.33      1.00\n",
+      " coefs[25]     -0.16      0.23     -0.16     -0.54      0.21    579.37      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.30    591.59      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.60      0.16   5125.28      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.60      1.64  11076.76      1.00\n",
+      " coefs[29]     -0.03      0.09     -0.03     -0.17      0.10    762.71      1.00\n",
+      " coefs[30]      0.05      0.09      0.05     -0.09      0.20    775.29      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.11      0.13    865.56      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.20    593.73      1.00\n",
+      " coefs[33]      0.14      0.13      0.14     -0.08      0.35    568.23      1.00\n",
+      " coefs[34]      0.11      0.05      0.10      0.03      0.19    939.36      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.04      0.73    567.29      1.00\n",
+      " coefs[36]      0.33      0.31      0.33     -0.16      0.83    557.88      1.00\n",
+      " coefs[37]      0.18      0.19      0.18     -0.12      0.50    561.91      1.00\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.06    987.06      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    660.49      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.13    719.50      1.00\n",
+      " coefs[41]     -0.78      0.58     -0.66     -1.62      0.03   5507.11      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.66      0.66    565.26      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    572.24      1.00\n",
+      " coefs[44]      0.17      0.21      0.17     -0.19      0.49    559.31      1.00\n",
+      " coefs[45]      0.13      0.29      0.13     -0.35      0.61    560.67      1.00\n",
+      " coefs[46]      0.23      0.27      0.24     -0.22      0.67    565.95      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    932.54      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.02    626.56      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4698.19      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4890.12      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.11    581.16      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.37      0.13    576.92      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.07    586.00      1.00\n",
+      " coefs[54]     -1.69      0.18     -1.68     -1.98     -1.39   4293.06      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 07 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.84      2.04   9250.39      1.00\n",
+      "  coefs[1]     -0.09      0.03     -0.09     -0.14     -0.03  11900.57      1.00\n",
+      "  coefs[2]     -0.07      0.06     -0.07     -0.18      0.03   3382.04      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.25   7273.45      1.00\n",
+      "  coefs[4]     -0.12      0.03     -0.12     -0.18     -0.07   8136.64      1.00\n",
+      "  coefs[5]     -0.08      0.03     -0.08     -0.14     -0.03  10454.22      1.00\n",
+      "  coefs[6]      0.18      0.25      0.17     -0.21      0.59   2678.54      1.00\n",
+      "  coefs[7]     -0.60      0.15     -0.60     -0.86     -0.37   2847.50      1.00\n",
+      "  coefs[8]      0.58      0.29      0.57      0.13      1.08   2654.20      1.00\n",
+      "  coefs[9]     -0.00      0.03     -0.00     -0.05      0.05  11135.80      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.64      1.49   2891.96      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.54      0.40   2908.39      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.96      1.18   2906.43      1.00\n",
+      " coefs[13]     -1.06      0.62     -1.00     -1.98      0.01   4513.52      1.00\n",
+      " coefs[14]     -0.45      0.68     -0.33     -1.50      0.58   5874.76      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.70     -1.69      0.00   4266.13      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.61     -1.61      0.10   5034.41      1.00\n",
+      " coefs[17]      0.03      0.17      0.03     -0.25      0.29    583.94      1.01\n",
+      " coefs[18]     -0.55      0.67     -0.42     -1.56      0.41   5785.31      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.36     -1.58      0.56   5403.98      1.00\n",
+      " coefs[20]     -0.76      0.58     -0.65     -1.60      0.04   5347.55      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1203.81      1.00\n",
+      " coefs[22]     -0.01      0.07     -0.00     -0.13      0.11    999.08      1.00\n",
+      " coefs[23]      0.18      0.25      0.19     -0.23      0.60    524.80      1.01\n",
+      " coefs[24]      0.08      0.16      0.08     -0.19      0.33    540.04      1.01\n",
+      " coefs[25]     -0.14      0.24     -0.14     -0.53      0.25    519.78      1.01\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.33      0.28    528.60      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.15   5063.80      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.60      1.66  10397.30      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    558.96      1.01\n",
+      " coefs[30]     -0.02      0.10     -0.02     -0.19      0.15    764.55      1.01\n",
+      " coefs[31]     -0.03      0.09     -0.03     -0.18      0.13   1073.59      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.10      0.20    533.20      1.01\n",
+      " coefs[33]      0.11      0.14      0.12     -0.10      0.34    521.92      1.01\n",
+      " coefs[34]      0.92      0.59      0.79      0.10      1.77   4646.56      1.00\n",
+      " coefs[35]      0.33      0.25      0.33     -0.08      0.73    510.92      1.01\n",
+      " coefs[36]      0.32      0.32      0.32     -0.22      0.83    510.46      1.01\n",
+      " coefs[37]      0.14      0.20      0.14     -0.21      0.45    510.92      1.01\n",
+      " coefs[38]     -0.07      0.05     -0.07     -0.15      0.01   1144.95      1.00\n",
+      " coefs[39]     -0.07      0.09     -0.07     -0.23      0.07    802.88      1.00\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    590.70      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.65      0.04   4782.36      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.66      0.74    511.47      1.01\n",
+      " coefs[43]     -0.01      0.24     -0.01     -0.41      0.37    519.40      1.01\n",
+      " coefs[44]      0.16      0.22      0.17     -0.22      0.50    513.40      1.01\n",
+      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    510.38      1.01\n",
+      " coefs[46]      0.21      0.29      0.22     -0.27      0.67    508.85      1.01\n",
+      " coefs[47]     -0.85      0.57     -0.73     -1.66     -0.05   4640.92      1.00\n",
+      " coefs[48]     -0.06      0.07     -0.06     -0.17      0.04    567.66      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.65     -0.00   4733.44      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4562.81      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.14     -0.42      0.15    524.03      1.01\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.33      0.21    517.19      1.01\n",
+      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.07    522.64      1.01\n",
+      " coefs[54]     -1.70      0.19     -1.69     -1.99     -1.39   3848.03      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 08 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.07      0.06      2.07      1.97      2.17   6006.90      1.00\n",
+      "  coefs[1]     -0.08      0.04     -0.08     -0.14     -0.02   6950.95      1.00\n",
+      "  coefs[2]     -0.02      0.07     -0.03     -0.15      0.10   2377.69      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   5572.29      1.00\n",
+      "  coefs[4]     -0.09      0.04     -0.09     -0.15     -0.03   5713.46      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.17     -0.22     -0.11   6679.18      1.00\n",
+      "  coefs[6]      0.41      0.30      0.40     -0.09      0.90   1949.82      1.00\n",
+      "  coefs[7]     -0.76      0.18     -0.75     -1.05     -0.45   2055.76      1.00\n",
+      "  coefs[8]      0.82      0.36      0.80      0.25      1.41   1971.61      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04   7249.79      1.00\n",
+      " coefs[10]      0.42      0.67      0.41     -0.62      1.57   2239.69      1.00\n",
+      " coefs[11]     -0.09      0.30     -0.10     -0.58      0.39   2251.76      1.00\n",
+      " coefs[12]      0.11      0.67      0.10     -0.95      1.24   2239.80      1.00\n",
+      " coefs[13]     -0.98      0.63     -0.92     -1.95      0.06   3243.72      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.53      0.52   3707.25      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.66      0.05   2946.07      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.61     -1.60      0.13   3752.58      1.00\n",
+      " coefs[17]     -0.13      0.19     -0.13     -0.46      0.16    896.44      1.01\n",
+      " coefs[18]     -0.55      0.67     -0.43     -1.56      0.44   4189.47      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.49      0.64   4551.92      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.64     -1.62      0.03   3922.11      1.00\n",
+      " coefs[21]     -0.76      0.59     -0.63     -1.61      0.05   3791.52      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.03      0.16    903.58      1.01\n",
+      " coefs[23]      0.10      0.25      0.10     -0.31      0.52    635.36      1.01\n",
+      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    629.98      1.01\n",
+      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    618.53      1.01\n",
+      " coefs[26]      0.01      0.18      0.01     -0.30      0.30    621.07      1.01\n",
+      " coefs[27]     -0.70      0.62     -0.57     -1.61      0.16   3618.38      1.00\n",
+      " coefs[28]     -0.77      0.60     -0.65     -1.61      0.03   3809.29      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    692.94      1.01\n",
+      " coefs[30]      0.11      0.09      0.11     -0.03      0.26    679.52      1.01\n",
+      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.07   3537.22      1.00\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.27    646.89      1.01\n",
+      " coefs[33]      0.19      0.13      0.19     -0.03      0.41    619.62      1.01\n",
+      " coefs[34]      0.10      0.05      0.10      0.01      0.18    970.71      1.00\n",
+      " coefs[35]      0.35      0.25      0.35     -0.04      0.77    606.18      1.01\n",
+      " coefs[36]      0.38      0.32      0.37     -0.14      0.90    604.82      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.14      0.51    610.69      1.01\n",
+      " coefs[38]     -0.77      0.57     -0.66     -1.58      0.02   3904.29      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    724.62      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    746.12      1.01\n",
+      " coefs[41]      0.04      0.06      0.04     -0.05      0.13    959.08      1.00\n",
+      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    605.63      1.01\n",
+      " coefs[43]      0.05      0.24      0.04     -0.33      0.44    609.63      1.01\n",
+      " coefs[44]      0.16      0.22      0.16     -0.20      0.52    605.83      1.01\n",
+      " coefs[45]      0.12      0.30      0.12     -0.40      0.60    602.34      1.01\n",
+      " coefs[46]      0.26      0.28      0.26     -0.21      0.72    603.36      1.01\n",
+      " coefs[47]     -0.08      0.07     -0.07     -0.19      0.04    976.89      1.00\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.23     -0.02    677.15      1.01\n",
+      " coefs[49]     -0.02      0.02     -0.02     -0.06      0.02   1377.67      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.71     -1.66     -0.07   3162.14      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.39      0.17    616.19      1.01\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.39      0.15    615.73      1.01\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.35      0.08    625.27      1.01\n",
+      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   2716.86      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 09 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.01      0.06      2.01      1.91      2.12   9583.20      1.00\n",
+      "  coefs[1]     -0.02      0.03     -0.02     -0.08      0.03  12244.17      1.00\n",
+      "  coefs[2]      0.00      0.07      0.00     -0.11      0.12   3899.89      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   7491.94      1.00\n",
+      "  coefs[4]     -0.06      0.03     -0.06     -0.11      0.00   8128.73      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  11573.08      1.00\n",
+      "  coefs[6]      0.41      0.27      0.41     -0.01      0.87   3193.36      1.00\n",
+      "  coefs[7]     -0.72      0.16     -0.72     -0.99     -0.46   3342.76      1.00\n",
+      "  coefs[8]      0.74      0.31      0.74      0.22      1.25   3174.21      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  11291.83      1.00\n",
+      " coefs[10]      0.42      0.66      0.41     -0.66      1.50   3092.99      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.07     -0.55      0.41   3105.34      1.00\n",
+      " coefs[12]      0.08      0.66      0.07     -0.95      1.21   3098.35      1.00\n",
+      " coefs[13]     -0.98      0.63     -0.92     -2.01      0.04   4969.90      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.54      0.49   6361.60      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.66     -1.67      0.07   4862.64      1.00\n",
+      " coefs[16]     -0.69      0.58     -0.58     -1.56      0.15   5141.14      1.00\n",
+      " coefs[17]     -0.11      0.19     -0.10     -0.42      0.20    969.52      1.00\n",
+      " coefs[18]     -0.54      0.67     -0.42     -1.59      0.42   5803.27      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.52      0.60   5673.56      1.00\n",
+      " coefs[20]      0.01      0.97      0.01     -1.58      1.61  11893.53      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1600.17      1.00\n",
+      " coefs[22]      0.13      0.05      0.13      0.04      0.21    754.02      1.00\n",
+      " coefs[23]      0.07      0.25      0.08     -0.35      0.47    676.30      1.00\n",
+      " coefs[24]      0.05      0.16      0.06     -0.21      0.31    649.22      1.00\n",
+      " coefs[25]     -0.07      0.24     -0.07     -0.45      0.32    638.48      1.00\n",
+      " coefs[26]      0.04      0.18      0.05     -0.26      0.34    635.07      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.58     -1.60      0.17   5073.59      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.61      1.64  10606.53      1.00\n",
+      " coefs[29]      0.07      0.08      0.08     -0.06      0.20    664.51      1.00\n",
+      " coefs[30]      0.02      0.10      0.02     -0.15      0.19    986.79      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.64     -1.60      0.08   4279.14      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    654.63      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    644.38      1.00\n",
+      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4721.10      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.05      0.76    626.40      1.00\n",
+      " coefs[36]      0.32      0.32      0.33     -0.23      0.81    621.11      1.00\n",
+      " coefs[37]      0.17      0.20      0.18     -0.17      0.49    620.09      1.00\n",
+      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    942.45      1.00\n",
+      " coefs[39]      0.05      0.07      0.05     -0.08      0.17    701.99      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.04      0.13    756.89      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.63      0.06   5097.00      1.00\n",
+      " coefs[42]      0.03      0.42      0.04     -0.69      0.70    616.88      1.00\n",
+      " coefs[43]      0.00      0.24      0.01     -0.39      0.39    616.74      1.00\n",
+      " coefs[44]      0.18      0.22      0.18     -0.19      0.53    626.94      1.00\n",
+      " coefs[45]      0.13      0.30      0.14     -0.38      0.62    622.26      1.00\n",
+      " coefs[46]      0.23      0.28      0.23     -0.25      0.69    622.08      1.00\n",
+      " coefs[47]     -0.09      0.09     -0.09     -0.23      0.05   1262.87      1.00\n",
+      " coefs[48]     -0.05      0.06     -0.05     -0.15      0.05    672.90      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.66     -0.01   4912.08      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4527.27      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.39      0.17    629.31      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.13    621.60      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    630.94      1.00\n",
+      " coefs[54]     -1.72      0.19     -1.70     -2.04     -1.42   3986.73      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 10 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.87      0.06      1.87      1.77      1.97   9851.85      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  12023.27      1.00\n",
+      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.03   3664.70      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8152.42      1.00\n",
+      "  coefs[4]     -0.11      0.03     -0.11     -0.17     -0.05   9085.34      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11119.98      1.00\n",
+      "  coefs[6]      0.03      0.25      0.02     -0.38      0.44   2855.36      1.00\n",
+      "  coefs[7]     -0.55      0.15     -0.54     -0.80     -0.30   3027.65      1.00\n",
+      "  coefs[8]      0.36      0.29      0.36     -0.12      0.83   2848.40      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  12091.31      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.70      1.43   3073.54      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.45   3091.90      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.96      1.17   3077.49      1.00\n",
+      " coefs[13]     -1.03      0.63     -0.97     -2.05     -0.03   5086.29      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.36     -1.52      0.54   5767.73      1.00\n",
+      " coefs[15]     -0.81      0.58     -0.70     -1.70      0.02   4429.92      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.62      0.10   5020.30      1.00\n",
+      " coefs[17]     -0.05      0.17     -0.05     -0.32      0.23    634.36      1.00\n",
+      " coefs[18]     -0.58      0.65     -0.47     -1.57      0.38   5653.50      1.00\n",
+      " coefs[19]     -0.49      0.68     -0.39     -1.57      0.56   5316.42      1.00\n",
+      " coefs[20]     -0.76      0.60     -0.64     -1.62      0.04   5141.74      1.00\n",
+      " coefs[21]      0.00      0.03      0.01     -0.04      0.06   1175.81      1.00\n",
+      " coefs[22]      0.09      0.05      0.09      0.00      0.17    589.10      1.00\n",
+      " coefs[23]      0.01      0.25      0.01     -0.39      0.42    537.95      1.00\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.29      0.23    562.57      1.00\n",
+      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.34    508.79      1.01\n",
+      " coefs[26]     -0.02      0.18     -0.02     -0.34      0.25    517.53      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.61      0.13   4770.04      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.55      1.72  10221.27      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.08      0.17    561.90      1.01\n",
+      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    748.10      1.00\n",
+      " coefs[31]     -0.01      0.08     -0.00     -0.13      0.12    783.81      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    532.06      1.01\n",
+      " coefs[33]      0.17      0.13      0.17     -0.06      0.37    514.16      1.01\n",
+      " coefs[34]      0.90      0.60      0.78      0.08      1.75   4699.27      1.00\n",
+      " coefs[35]      0.28      0.24      0.28     -0.10      0.69    505.90      1.01\n",
+      " coefs[36]      0.33      0.31      0.34     -0.17      0.84    505.30      1.01\n",
+      " coefs[37]      0.16      0.19      0.16     -0.16      0.47    503.53      1.01\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    827.64      1.00\n",
+      " coefs[39]     -0.03      0.08     -0.03     -0.16      0.11    663.60      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    666.94      1.00\n",
+      " coefs[41]     -0.81      0.59     -0.68     -1.71     -0.03   4477.38      1.00\n",
+      " coefs[42]      0.06      0.41      0.07     -0.61      0.73    504.16      1.01\n",
+      " coefs[43]      0.03      0.23      0.04     -0.35      0.41    506.87      1.01\n",
+      " coefs[44]      0.20      0.21      0.20     -0.14      0.55    502.28      1.01\n",
+      " coefs[45]      0.08      0.30      0.09     -0.40      0.57    503.49      1.01\n",
+      " coefs[46]      0.17      0.28      0.18     -0.29      0.62    501.86      1.01\n",
+      " coefs[47]     -0.09      0.07     -0.08     -0.20      0.03    751.62      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    553.11      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.01   4806.02      1.00\n",
+      " coefs[50]     -0.83      0.59     -0.70     -1.67     -0.03   4711.38      1.00\n",
+      " coefs[51]     -0.08      0.17     -0.08     -0.36      0.18    505.60      1.01\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.32      0.19    510.68      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.01    515.18      1.01\n",
+      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.33   4089.82      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 11 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.92      0.06      1.92      1.82      2.02  10396.90      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.08      0.03  11519.16      1.00\n",
+      "  coefs[2]     -0.06      0.06     -0.06     -0.16      0.04   4117.58      1.00\n",
+      "  coefs[3]     -0.29      0.03     -0.29     -0.35     -0.23   7737.34      1.00\n",
+      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8773.20      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.18     -0.22     -0.12  11016.25      1.00\n",
+      "  coefs[6]      0.19      0.21      0.18     -0.16      0.50   2829.57      1.00\n",
+      "  coefs[7]     -0.59      0.13     -0.58     -0.79     -0.38   3123.90      1.00\n",
+      "  coefs[8]      0.48      0.24      0.46      0.09      0.85   2830.52      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.09      0.00  12268.23      1.00\n",
+      " coefs[10]      0.45      0.66      0.44     -0.64      1.53   3044.65      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.56      0.40   3052.36      1.00\n",
+      " coefs[12]      0.08      0.65      0.07     -1.01      1.15   3041.06      1.00\n",
+      " coefs[13]     -1.03      0.62     -0.97     -2.08     -0.06   4562.95      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.35     -1.55      0.51   5903.18      1.00\n",
+      " coefs[15]     -0.80      0.56     -0.70     -1.67      0.02   4665.74      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.63      0.10   4957.23      1.00\n",
+      " coefs[17]      0.00      0.17      0.00     -0.27      0.28    610.13      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.41   5781.93      1.00\n",
+      " coefs[19]     -0.46      0.67     -0.37     -1.56      0.55   6074.50      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.03   5252.85      1.00\n",
+      " coefs[21]     -0.00      0.03     -0.00     -0.05      0.05   1165.34      1.00\n",
+      " coefs[22]      0.05      0.05      0.06     -0.04      0.14    680.97      1.00\n",
+      " coefs[23]      0.09      0.25      0.10     -0.34      0.48    529.12      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.01     -0.27      0.25    558.96      1.00\n",
+      " coefs[25]     -0.03      0.23     -0.02     -0.43      0.35    525.19      1.00\n",
+      " coefs[26]      0.06      0.18      0.07     -0.23      0.36    518.36      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.62      0.13   4954.67      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.61      1.65  10846.53      1.00\n",
+      " coefs[29]      0.05      0.08      0.06     -0.08      0.18    563.62      1.00\n",
+      " coefs[30]     -0.05      0.10     -0.04     -0.22      0.11    807.13      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.65     -1.62      0.03   4982.14      1.00\n",
+      " coefs[32]      0.09      0.09      0.10     -0.06      0.24    543.12      1.00\n",
+      " coefs[33]      0.14      0.13      0.14     -0.08      0.36    525.64      1.00\n",
+      " coefs[34]      0.16      0.06      0.15      0.06      0.26   1251.32      1.00\n",
+      " coefs[35]      0.38      0.25      0.39     -0.01      0.81    516.49      1.00\n",
+      " coefs[36]      0.34      0.31      0.35     -0.19      0.85    511.53      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.14      0.51    514.24      1.00\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.07      0.05    703.70      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    596.82      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.15    671.03      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   4996.10      1.00\n",
+      " coefs[42]      0.08      0.42      0.09     -0.63      0.76    512.64      1.00\n",
+      " coefs[43]      0.00      0.23      0.01     -0.38      0.40    516.39      1.00\n",
+      " coefs[44]      0.18      0.22      0.18     -0.18      0.53    514.45      1.00\n",
+      " coefs[45]      0.15      0.30      0.16     -0.35      0.64    513.91      1.00\n",
+      " coefs[46]      0.23      0.28      0.24     -0.24      0.69    514.26      1.00\n",
+      " coefs[47]     -0.85      0.57     -0.72     -1.67     -0.04   4633.11      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.18      0.03    600.11      1.00\n",
+      " coefs[49]     -0.80      0.60     -0.68     -1.64      0.00   4628.84      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.67     -0.09   4617.98      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.09     -0.40      0.17    524.69      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.40      0.14    525.01      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.12     -0.34      0.09    532.74      1.00\n",
+      " coefs[54]     -1.74      0.19     -1.73     -2.04     -1.43   3929.35      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 12 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.93      2.14   8304.52      1.00\n",
+      "  coefs[1]     -0.01      0.04     -0.01     -0.06      0.06  10118.62      1.00\n",
+      "  coefs[2]     -0.12      0.07     -0.11     -0.24     -0.00   3682.19      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   6963.70      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.15     -0.04   7744.04      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.09  10497.57      1.00\n",
+      "  coefs[6]      0.11      0.28      0.11     -0.34      0.58   2964.29      1.00\n",
+      "  coefs[7]     -0.58      0.17     -0.58     -0.85     -0.29   3083.36      1.00\n",
+      "  coefs[8]      0.40      0.33      0.39     -0.15      0.92   2948.26      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  10148.21      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.72      1.41   3238.54      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3251.02      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -0.94      1.19   3237.31      1.00\n",
+      " coefs[13]     -1.00      0.63     -0.94     -2.09     -0.05   4687.49      1.00\n",
+      " coefs[14]     -0.44      0.67     -0.34     -1.50      0.56   6099.61      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.07   4550.37      1.00\n",
+      " coefs[16]     -0.71      0.58     -0.60     -1.61      0.12   4864.50      1.00\n",
+      " coefs[17]     -0.13      0.19     -0.12     -0.45      0.19    940.69      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.43     -1.56      0.40   5805.63      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.35     -1.59      0.55   5277.45      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   4861.90      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5058.03      1.00\n",
+      " coefs[22]      0.10      0.05      0.10      0.02      0.19    791.84      1.00\n",
+      " coefs[23]      0.10      0.25      0.10     -0.30      0.52    650.30      1.00\n",
+      " coefs[24]      0.12      0.16      0.12     -0.14      0.38    644.67      1.00\n",
+      " coefs[25]     -0.01      0.24     -0.00     -0.39      0.38    630.09      1.00\n",
+      " coefs[26]      0.11      0.18      0.12     -0.17      0.43    635.35      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.63      0.14   4712.25      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.60      1.67  10040.11      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.07      0.18    679.39      1.00\n",
+      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    786.03      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.63      0.06   5149.75      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.06      0.24    650.45      1.00\n",
+      " coefs[33]      0.13      0.14      0.13     -0.07      0.37    630.38      1.00\n",
+      " coefs[34]      0.14      0.06      0.13      0.03      0.24   1370.58      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.04      0.78    620.21      1.00\n",
+      " coefs[36]      0.36      0.32      0.36     -0.16      0.89    619.37      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.15      0.51    624.44      1.00\n",
+      " coefs[38]     -0.04      0.05     -0.03     -0.11      0.04   1296.38      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    734.11      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    758.44      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.65      0.02   5148.08      1.00\n",
+      " coefs[42]      0.12      0.43      0.13     -0.57      0.81    620.28      1.00\n",
+      " coefs[43]      0.03      0.24      0.03     -0.36      0.41    626.67      1.00\n",
+      " coefs[44]      0.15      0.22      0.16     -0.20      0.52    626.95      1.00\n",
+      " coefs[45]      0.10      0.31      0.11     -0.38      0.61    624.04      1.00\n",
+      " coefs[46]      0.22      0.29      0.23     -0.24      0.70    618.56      1.00\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.18      0.05    994.64      1.00\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.01    668.23      1.00\n",
+      " coefs[49]     -0.79      0.59     -0.68     -1.64      0.00   4915.15      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.71     -1.69     -0.05   4731.62      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.20    629.43      1.00\n",
+      " coefs[52]     -0.05      0.16     -0.04     -0.31      0.22    625.15      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.13     -0.35      0.08    645.94      1.00\n",
+      " coefs[54]     -1.73      0.19     -1.71     -2.03     -1.42   3867.53      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 13 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.06      0.06      2.06      1.96      2.16  10107.97      1.00\n",
+      "  coefs[1]     -0.07      0.04     -0.07     -0.12     -0.01  12223.43      1.00\n",
+      "  coefs[2]     -0.21      0.07     -0.21     -0.33     -0.08   3247.79      1.00\n",
+      "  coefs[3]     -0.34      0.03     -0.34     -0.40     -0.28   7744.39      1.00\n",
+      "  coefs[4]     -0.11      0.04     -0.11     -0.17     -0.05   8886.81      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  10594.79      1.00\n",
+      "  coefs[6]     -0.08      0.30     -0.08     -0.56      0.41   2710.82      1.00\n",
+      "  coefs[7]     -0.52      0.18     -0.52     -0.82     -0.23   2838.19      1.00\n",
+      "  coefs[8]      0.17      0.35      0.17     -0.39      0.74   2697.80      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.08      0.02  11093.40      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.67      1.48   3051.80      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.52      0.43   3043.81      1.00\n",
+      " coefs[12]      0.06      0.65      0.06     -1.06      1.08   3055.42      1.00\n",
+      " coefs[13]     -0.91      0.65     -0.86     -1.95      0.15   4747.74      1.00\n",
+      " coefs[14]     -0.48      0.66     -0.37     -1.53      0.49   5540.97      1.00\n",
+      " coefs[15]     -0.77      0.56     -0.67     -1.63      0.05   4870.06      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.59      0.14   4957.56      1.00\n",
+      " coefs[17]     -0.06      0.18     -0.05     -0.34      0.23    543.36      1.01\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.40   5806.90      1.00\n",
+      " coefs[19]     -0.49      0.67     -0.39     -1.56      0.58   5841.70      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5195.52      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.05      0.06   1082.76      1.00\n",
+      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    592.12      1.01\n",
+      " coefs[23]     -0.10      0.26     -0.10     -0.52      0.32    461.09      1.01\n",
+      " coefs[24]      0.00      0.16      0.00     -0.26      0.26    453.93      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.44      0.32    426.89      1.01\n",
+      " coefs[26]      0.06      0.18      0.06     -0.25      0.35    434.65      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.14   5038.79      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.69      1.60  11808.60      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.10      0.16    486.47      1.01\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.31      0.10   1023.19      1.01\n",
+      " coefs[31]      0.02      0.08      0.02     -0.11      0.15    677.56      1.01\n",
+      " coefs[32]      0.07      0.09      0.08     -0.07      0.22    442.33      1.01\n",
+      " coefs[33]      0.13      0.13      0.14     -0.08      0.35    431.07      1.01\n",
+      " coefs[34]      0.91      0.60      0.79      0.11      1.80   5008.02      1.00\n",
+      " coefs[35]      0.31      0.25      0.31     -0.09      0.70    419.67      1.01\n",
+      " coefs[36]      0.32      0.31      0.32     -0.21      0.81    421.90      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.15      0.49    426.28      1.01\n",
+      " coefs[38]     -0.06      0.05     -0.05     -0.13      0.02   1113.26      1.00\n",
+      " coefs[39]      0.03      0.08      0.03     -0.09      0.16    480.00      1.01\n",
+      " coefs[40]      0.10      0.05      0.10      0.02      0.19    500.83      1.01\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1035.85      1.01\n",
+      " coefs[42]     -0.00      0.42      0.00     -0.70      0.67    423.22      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.40      0.36    427.20      1.01\n",
+      " coefs[44]      0.18      0.22      0.18     -0.17      0.53    421.49      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.42      0.56    416.39      1.01\n",
+      " coefs[46]      0.22      0.28      0.22     -0.25      0.66    423.39      1.01\n",
+      " coefs[47]     -0.06      0.07     -0.06     -0.17      0.06    637.28      1.01\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    457.03      1.01\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.00   4772.50      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.75     -1.69     -0.07   4318.31      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.13    423.95      1.01\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.13    434.85      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.19     -0.40      0.02    437.62      1.01\n",
+      " coefs[54]     -1.71      0.19     -1.69     -2.01     -1.41   4099.94      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 14 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.08   9005.66      1.00\n",
+      "  coefs[1]     -0.02      0.03     -0.02     -0.07      0.04  11557.78      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.16      0.05   4138.63      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7839.59      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8500.08      1.00\n",
+      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  10663.93      1.00\n",
+      "  coefs[6]      0.14      0.25      0.13     -0.25      0.55   3159.51      1.00\n",
+      "  coefs[7]     -0.61      0.15     -0.60     -0.85     -0.36   3309.15      1.00\n",
+      "  coefs[8]      0.47      0.29      0.46     -0.03      0.91   3123.20      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.05  11937.39      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.71      1.44   3091.25      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.06     -0.57      0.39   3085.88      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -1.03      1.11   3094.82      1.00\n",
+      " coefs[13]     -1.02      0.63     -0.96     -2.08     -0.04   5050.19      1.00\n",
+      " coefs[14]     -0.47      0.68     -0.36     -1.53      0.53   5346.83      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.64      0.05   4722.58      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.62      0.11   4855.77      1.00\n",
+      " coefs[17]     -0.03      0.18     -0.03     -0.31      0.27    720.50      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.43   6038.97      1.00\n",
+      " coefs[19]     -0.47      0.69     -0.38     -1.51      0.66   5416.81      1.00\n",
+      " coefs[20]      0.02      0.98      0.01     -1.59      1.63  13208.44      1.00\n",
+      " coefs[21]      0.02      0.99      0.02     -1.54      1.70  10823.00      1.00\n",
+      " coefs[22]     -0.02      0.07     -0.01     -0.13      0.10   1087.05      1.00\n",
+      " coefs[23]      0.05      0.25      0.05     -0.36      0.48    562.53      1.00\n",
+      " coefs[24]     -0.06      0.17     -0.06     -0.34      0.21    601.03      1.00\n",
+      " coefs[25]     -0.06      0.24     -0.05     -0.46      0.34    550.41      1.00\n",
+      " coefs[26]      0.07      0.19      0.07     -0.23      0.38    546.27      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.61      0.15   4953.64      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.57      1.67  10744.99      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    590.76      1.00\n",
+      " coefs[30]      0.02      0.10      0.03     -0.14      0.18    710.84      1.00\n",
+      " coefs[31]     -0.78      0.58     -0.66     -1.62      0.05   5056.04      1.00\n",
+      " coefs[32]      0.04      0.09      0.04     -0.11      0.20    568.43      1.00\n",
+      " coefs[33]      0.15      0.14      0.15     -0.06      0.39    546.49      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.11      1.78   4921.83      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.08      0.74    542.19      1.00\n",
+      " coefs[36]      0.33      0.32      0.33     -0.19      0.88    538.22      1.00\n",
+      " coefs[37]      0.13      0.20      0.13     -0.19      0.48    539.85      1.00\n",
+      " coefs[38]      0.02      0.04      0.02     -0.05      0.10   1055.60      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.14    606.11      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.03      0.14    634.23      1.00\n",
+      " coefs[41]      0.02      0.06      0.03     -0.07      0.12    852.14      1.00\n",
+      " coefs[42]      0.07      0.43      0.08     -0.65      0.77    540.64      1.00\n",
+      " coefs[43]     -0.04      0.24     -0.04     -0.44      0.35    546.56      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.19      0.53    536.30      1.00\n",
+      " coefs[45]      0.11      0.31      0.11     -0.39      0.64    535.15      1.00\n",
+      " coefs[46]      0.18      0.29      0.18     -0.30      0.65    540.24      1.00\n",
+      " coefs[47]     -0.02      0.06     -0.01     -0.12      0.09    669.38      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.03    578.06      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.66      0.02   4966.31      1.00\n",
+      " coefs[50]     -0.84      0.58     -0.71     -1.69     -0.06   5157.37      1.00\n",
+      " coefs[51]     -0.05      0.18     -0.04     -0.34      0.24    549.11      1.00\n",
+      " coefs[52]     -0.13      0.17     -0.13     -0.41      0.13    546.42      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.39      0.05    554.62      1.00\n",
+      " coefs[54]     -1.64      0.19     -1.63     -1.95     -1.34   4052.25      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 15 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.05      0.06      2.05      1.94      2.14   9177.00      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.00  11743.81      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.02   3628.73      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.38     -0.27   7842.18      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8649.39      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  10859.96      1.00\n",
+      "  coefs[6]      0.37      0.27      0.36     -0.08      0.79   2752.83      1.00\n",
+      "  coefs[7]     -0.83      0.16     -0.83     -1.09     -0.56   2920.83      1.00\n",
+      "  coefs[8]      0.83      0.31      0.82      0.31      1.33   2750.68      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11841.94      1.00\n",
+      " coefs[10]      0.40      0.65      0.39     -0.70      1.44   3135.56      1.00\n",
+      " coefs[11]     -0.01      0.29     -0.02     -0.49      0.47   3135.50      1.00\n",
+      " coefs[12]      0.15      0.65      0.14     -0.89      1.24   3127.87      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.01     -2.06     -0.10   5383.26      1.00\n",
+      " coefs[14]     -0.45      0.66     -0.34     -1.47      0.56   5506.65      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.68     -1.68      0.01   4585.23      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.59      0.12   5284.94      1.00\n",
+      " coefs[17]     -0.27      0.22     -0.26     -0.63      0.09   1153.36      1.00\n",
+      " coefs[18]     -0.52      0.67     -0.41     -1.54      0.47   5888.75      1.00\n",
+      " coefs[19]     -0.45      0.68     -0.36     -1.55      0.63   6200.15      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   4811.83      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.67     -1.64      0.01   4300.73      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.04      0.15    790.42      1.01\n",
+      " coefs[23]      0.22      0.24      0.21     -0.16      0.62    521.03      1.01\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.28      0.23    561.51      1.01\n",
+      " coefs[25]     -0.05      0.23     -0.05     -0.42      0.32    512.26      1.01\n",
+      " coefs[26]      0.00      0.18      0.00     -0.28      0.29    515.81      1.01\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.13   5153.89      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.60      1.67  11091.19      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.12      0.14    604.99      1.01\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.29      0.12   1242.60      1.00\n",
+      " coefs[31]      0.04      0.07      0.04     -0.09      0.15    737.77      1.01\n",
+      " coefs[32]      0.05      0.09      0.05     -0.09      0.19    527.77      1.01\n",
+      " coefs[33]      0.14      0.13      0.14     -0.06      0.35    518.80      1.01\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.76   4699.77      1.00\n",
+      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    503.71      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.20      0.79    506.01      1.01\n",
+      " coefs[37]      0.10      0.19      0.10     -0.22      0.41    509.89      1.01\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    903.45      1.01\n",
+      " coefs[39]      0.05      0.07      0.05     -0.06      0.17    542.48      1.01\n",
+      " coefs[40]      0.04      0.05      0.04     -0.05      0.12    655.54      1.01\n",
+      " coefs[41]      0.02      0.05      0.02     -0.07      0.10    905.27      1.01\n",
+      " coefs[42]      0.04      0.41      0.04     -0.61      0.71    503.61      1.01\n",
+      " coefs[43]     -0.00      0.23     -0.00     -0.37      0.37    512.92      1.01\n",
+      " coefs[44]      0.16      0.21      0.15     -0.17      0.51    504.57      1.01\n",
+      " coefs[45]      0.07      0.29      0.07     -0.40      0.55    502.69      1.01\n",
+      " coefs[46]      0.18      0.27      0.18     -0.25      0.64    506.09      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.18      0.04    782.66      1.01\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    544.83      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.63      0.02   4838.35      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.75     -1.69     -0.08   4164.47      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.36      0.18    515.73      1.01\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.38      0.13    507.39      1.01\n",
+      " coefs[53]     -0.19      0.13     -0.19     -0.40      0.01    515.72      1.01\n",
+      " coefs[54]     -1.66      0.18     -1.64     -1.96     -1.36   4343.76      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 16 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9179.36      1.00\n",
+      "  coefs[1]      0.01      0.03      0.01     -0.05      0.07  10791.72      1.00\n",
+      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3510.14      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   7615.67      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8998.44      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10867.82      1.00\n",
+      "  coefs[6]      0.50      0.29      0.49      0.02      0.99   2920.24      1.00\n",
+      "  coefs[7]     -0.79      0.18     -0.79     -1.08     -0.48   3039.41      1.00\n",
+      "  coefs[8]      0.87      0.35      0.86      0.27      1.42   2922.72      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11173.31      1.00\n",
+      " coefs[10]      0.46      0.65      0.45     -0.57      1.54   3308.73      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.43   3324.22      1.00\n",
+      " coefs[12]      0.08      0.65      0.08     -0.96      1.14   3310.11      1.00\n",
+      " coefs[13]     -1.05      0.62     -0.99     -2.00     -0.03   4531.52      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.51      0.52   5577.25      1.00\n",
+      " coefs[15]     -0.78      0.58     -0.68     -1.64      0.08   4391.98      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.57      0.15   4813.23      1.00\n",
+      " coefs[17]     -0.29      0.22     -0.28     -0.65      0.08   1050.49      1.00\n",
+      " coefs[18]     -0.55      0.67     -0.43     -1.57      0.42   5579.16      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.60      0.54   5415.16      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.01   5013.34      1.00\n",
+      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.03   4630.94      1.00\n",
+      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    831.29      1.00\n",
+      " coefs[23]      0.12      0.24      0.12     -0.28      0.51    565.03      1.01\n",
+      " coefs[24]      0.10      0.15      0.11     -0.14      0.36    566.50      1.01\n",
+      " coefs[25]     -0.06      0.23     -0.06     -0.44      0.31    544.78      1.01\n",
+      " coefs[26]      0.04      0.18      0.04     -0.25      0.33    556.89      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.60     -1.59      0.13   4905.08      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.69  10411.65      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    596.47      1.01\n",
+      " coefs[30]      0.04      0.09      0.04     -0.11      0.18    684.25      1.00\n",
+      " coefs[31]      0.04      0.07      0.04     -0.07      0.15    717.08      1.01\n",
+      " coefs[32]      0.09      0.09      0.10     -0.06      0.23    560.88      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.06      0.36    550.32      1.01\n",
+      " coefs[34]      0.90      0.60      0.79      0.09      1.79   4522.53      1.00\n",
+      " coefs[35]      0.33      0.24      0.33     -0.06      0.72    542.54      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.19      0.81    538.21      1.01\n",
+      " coefs[37]      0.17      0.19      0.18     -0.16      0.47    545.27      1.01\n",
+      " coefs[38]      0.01      0.04      0.01     -0.05      0.07    873.71      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.11      0.15    679.04      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.05      0.10    628.08      1.01\n",
+      " coefs[41]     -0.80      0.59     -0.67     -1.67      0.03   4771.75      1.00\n",
+      " coefs[42]      0.02      0.41      0.03     -0.65      0.68    537.69      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.38      0.36    545.99      1.01\n",
+      " coefs[44]      0.19      0.21      0.19     -0.18      0.51    539.59      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.41      0.55    540.83      1.01\n",
+      " coefs[46]      0.22      0.28      0.23     -0.23      0.66    538.97      1.01\n",
+      " coefs[47]     -0.02      0.07     -0.02     -0.13      0.09    789.16      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.04    598.54      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.65      0.02   4719.61      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.70     -0.07   4374.23      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    547.36      1.01\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.16    550.52      1.01\n",
+      " coefs[53]     -0.12      0.13     -0.12     -0.33      0.08    546.83      1.01\n",
+      " coefs[54]     -1.68      0.18     -1.67     -1.98     -1.38   3683.28      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 17 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.12   9825.76      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.01  11491.29      1.00\n",
+      "  coefs[2]     -0.12      0.07     -0.12     -0.24     -0.02   4035.17      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.37     -0.26   7508.58      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.13     -0.02   8850.54      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.07  10832.36      1.00\n",
+      "  coefs[6]     -0.03      0.25     -0.03     -0.43      0.39   3103.03      1.00\n",
+      "  coefs[7]     -0.49      0.15     -0.49     -0.74     -0.24   3302.29      1.00\n",
+      "  coefs[8]      0.26      0.29      0.26     -0.20      0.74   3075.37      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.12     -0.03  11096.54      1.00\n",
+      " coefs[10]      0.47      0.64      0.47     -0.61      1.49   3268.81      1.00\n",
+      " coefs[11]     -0.08      0.29     -0.08     -0.59      0.35   3299.38      1.00\n",
+      " coefs[12]      0.07      0.64      0.06     -1.04      1.07   3296.69      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.07     -0.09   4800.78      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.52   5846.17      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.69     -1.62      0.06   4206.97      1.00\n",
+      " coefs[16]     -0.71      0.58     -0.60     -1.58      0.14   5088.30      1.00\n",
+      " coefs[17]     -0.05      0.18     -0.05     -0.33      0.24    599.68      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.45   5927.75      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.58   5998.88      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.67     -1.62      0.01   4825.52      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1133.37      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    589.43      1.01\n",
+      " coefs[23]      0.15      0.25      0.15     -0.26      0.56    468.13      1.01\n",
+      " coefs[24]      0.13      0.16      0.13     -0.14      0.37    471.51      1.01\n",
+      " coefs[25]     -0.03      0.23     -0.03     -0.41      0.36    459.24      1.01\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    473.85      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.62      0.14   4955.11      1.00\n",
+      " coefs[28]      0.01      0.99      0.01     -1.53      1.73  10769.97      1.00\n",
+      " coefs[29]     -0.00      0.08     -0.01     -0.13      0.13    522.04      1.01\n",
+      " coefs[30]      0.11      0.09      0.11     -0.04      0.25    527.10      1.01\n",
+      " coefs[31]      0.04      0.07      0.04     -0.08      0.16    648.90      1.01\n",
+      " coefs[32]      0.10      0.09      0.10     -0.04      0.25    479.99      1.01\n",
+      " coefs[33]      0.12      0.13      0.12     -0.10      0.34    472.55      1.01\n",
+      " coefs[34]      0.11      0.05      0.11      0.03      0.20    757.54      1.01\n",
+      " coefs[35]      0.29      0.25      0.29     -0.10      0.70    452.91      1.01\n",
+      " coefs[36]      0.34      0.31      0.34     -0.21      0.83    453.74      1.01\n",
+      " coefs[37]      0.16      0.20      0.16     -0.17      0.48    458.11      1.01\n",
+      " coefs[38]     -0.01      0.04     -0.01     -0.08      0.05    759.34      1.01\n",
+      " coefs[39]     -0.03      0.08     -0.03     -0.17      0.10    622.87      1.01\n",
+      " coefs[40]      0.08      0.05      0.08     -0.00      0.17    627.81      1.01\n",
+      " coefs[41]     -0.78      0.60     -0.66     -1.68      0.02   5038.60      1.00\n",
+      " coefs[42]     -0.02      0.42     -0.02     -0.68      0.70    454.27      1.01\n",
+      " coefs[43]     -0.05      0.23     -0.05     -0.44      0.33    462.64      1.01\n",
+      " coefs[44]      0.19      0.22      0.18     -0.17      0.54    455.92      1.01\n",
+      " coefs[45]      0.11      0.30      0.11     -0.40      0.59    455.52      1.01\n",
+      " coefs[46]      0.20      0.28      0.20     -0.28      0.64    452.79      1.01\n",
+      " coefs[47]     -0.03      0.07     -0.03     -0.14      0.08    647.18      1.01\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.02    503.96      1.01\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.66     -0.01   4790.18      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.73     -1.69     -0.06   4353.25      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.16    465.74      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.39      0.14    460.95      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.42      0.01    466.41      1.01\n",
+      " coefs[54]     -1.69      0.18     -1.67     -1.97     -1.38   4247.42      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 18 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.01      0.06      2.01      1.91      2.11   9222.07      1.00\n",
+      "  coefs[1]     -0.07      0.03     -0.07     -0.13     -0.02  11037.73      1.00\n",
+      "  coefs[2]     -0.11      0.06     -0.11     -0.22     -0.01   3896.77      1.00\n",
+      "  coefs[3]     -0.38      0.03     -0.38     -0.44     -0.33   7697.55      1.00\n",
+      "  coefs[4]     -0.04      0.03     -0.05     -0.10      0.01   8703.86      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10405.15      1.00\n",
+      "  coefs[6]      0.12      0.23      0.12     -0.24      0.51   2968.23      1.00\n",
+      "  coefs[7]     -0.60      0.14     -0.60     -0.83     -0.36   3184.79      1.00\n",
+      "  coefs[8]      0.42      0.27      0.42     -0.02      0.86   2967.49      1.00\n",
+      "  coefs[9]      0.03      0.03      0.03     -0.02      0.08  11147.01      1.00\n",
+      " coefs[10]      0.44      0.65      0.44     -0.67      1.48   2962.23      1.00\n",
+      " coefs[11]     -0.08      0.29     -0.08     -0.56      0.40   2974.48      1.00\n",
+      " coefs[12]      0.07      0.65      0.07     -1.00      1.15   2969.88      1.00\n",
+      " coefs[13]     -0.99      0.64     -0.93     -2.05      0.01   4667.16      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.52   5983.57      1.00\n",
+      " coefs[15]     -0.78      0.58     -0.67     -1.66      0.06   4759.51      1.00\n",
+      " coefs[16]     -0.70      0.58     -0.60     -1.57      0.13   5111.37      1.00\n",
+      " coefs[17]     -0.02      0.17     -0.02     -0.30      0.25    723.30      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   5519.08      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.58      0.55   5869.82      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.67     -1.63      0.01   4721.83      1.00\n",
+      " coefs[21]     -0.77      0.58     -0.66     -1.60      0.03   5203.05      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.16    742.09      1.01\n",
+      " coefs[23]      0.05      0.25      0.05     -0.36      0.45    635.21      1.01\n",
+      " coefs[24]     -0.03      0.16     -0.03     -0.30      0.22    658.36      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.30    612.30      1.01\n",
+      " coefs[26]      0.04      0.18      0.05     -0.26      0.33    624.90      1.01\n",
+      " coefs[27]     -0.70      0.62     -0.58     -1.60      0.17   5010.88      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.62      1.66  10001.87      1.00\n",
+      " coefs[29]      0.03      0.08      0.03     -0.11      0.15    670.66      1.01\n",
+      " coefs[30]      0.07      0.09      0.07     -0.09      0.21    741.75      1.01\n",
+      " coefs[31]     -0.00      0.08     -0.00     -0.13      0.12    871.75      1.01\n",
+      " coefs[32]      0.12      0.09      0.12     -0.03      0.26    641.81      1.01\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    606.63      1.01\n",
+      " coefs[34]      0.15      0.06      0.14      0.05      0.25   1321.74      1.00\n",
+      " coefs[35]      0.33      0.24      0.33     -0.08      0.71    602.00      1.01\n",
+      " coefs[36]      0.33      0.31      0.33     -0.17      0.84    599.72      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.14      0.50    607.37      1.01\n",
+      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    825.58      1.01\n",
+      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    688.22      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.05      0.11    737.72      1.01\n",
+      " coefs[41]      0.01      0.07      0.02     -0.10      0.12   1492.59      1.00\n",
+      " coefs[42]      0.02      0.41      0.02     -0.68      0.69    602.54      1.01\n",
+      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.34    613.82      1.01\n",
+      " coefs[44]      0.19      0.21      0.19     -0.16      0.54    604.50      1.01\n",
+      " coefs[45]      0.13      0.30      0.14     -0.39      0.59    603.75      1.01\n",
+      " coefs[46]      0.23      0.28      0.23     -0.23      0.68    609.11      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.06     -0.18      0.05    933.07      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    672.42      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.65      0.00   4630.65      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4276.88      1.00\n",
+      " coefs[51]     -0.07      0.17     -0.07     -0.35      0.21    624.71      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.40      0.12    615.24      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    608.75      1.01\n",
+      " coefs[54]     -1.65      0.19     -1.64     -1.94     -1.35   3844.77      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 19 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.09      0.06      2.09      1.99      2.20   9900.43      1.00\n",
+      "  coefs[1]     -0.09      0.04     -0.09     -0.15     -0.03  12225.38      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3777.37      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   8256.62      1.00\n",
+      "  coefs[4]     -0.13      0.04     -0.13     -0.18     -0.07   9095.25      1.00\n",
+      "  coefs[5]     -0.20      0.03     -0.20     -0.25     -0.15  11139.58      1.00\n",
+      "  coefs[6]      0.43      0.28      0.42     -0.03      0.90   3032.91      1.00\n",
+      "  coefs[7]     -0.85      0.17     -0.84     -1.13     -0.56   3189.63      1.00\n",
+      "  coefs[8]      0.87      0.33      0.86      0.30      1.40   3022.08      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  12442.31      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.72      1.41   3331.08      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.07     -0.54      0.41   3341.18      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -1.03      1.10   3333.96      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.01     -2.05     -0.08   5218.74      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.54      0.52   5822.97      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.68     -1.65      0.06   4591.28      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.61     -1.62      0.14   5379.81      1.00\n",
+      " coefs[17]      0.00      0.17      0.01     -0.26      0.29    769.45      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.56      0.42   6037.22      1.00\n",
+      " coefs[19]     -0.44      0.68     -0.36     -1.52      0.62   6056.28      1.00\n",
+      " coefs[20]     -0.77      0.60     -0.65     -1.63      0.03   4989.46      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06   1593.75      1.00\n",
+      " coefs[22]      0.09      0.05      0.10      0.01      0.18    737.03      1.00\n",
+      " coefs[23]      0.20      0.25      0.21     -0.21      0.61    633.08      1.00\n",
+      " coefs[24]      0.08      0.16      0.09     -0.17      0.34    632.23      1.00\n",
+      " coefs[25]     -0.10      0.24     -0.10     -0.46      0.31    630.33      1.00\n",
+      " coefs[26]      0.08      0.18      0.08     -0.21      0.39    615.33      1.00\n",
+      " coefs[27]     -0.67      0.63     -0.55     -1.59      0.22   5405.23      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.67      1.63  11841.95      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.13      0.13    726.36      1.00\n",
+      " coefs[30]      0.10      0.09      0.10     -0.05      0.23    715.32      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1298.58      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    653.45      1.00\n",
+      " coefs[33]      0.11      0.13      0.11     -0.12      0.32    620.44      1.00\n",
+      " coefs[34]      0.93      0.59      0.82      0.12      1.77   4759.24      1.00\n",
+      " coefs[35]      0.35      0.25      0.36     -0.04      0.76    611.41      1.00\n",
+      " coefs[36]      0.34      0.31      0.35     -0.18      0.84    609.07      1.00\n",
+      " coefs[37]      0.18      0.20      0.18     -0.16      0.49    617.89      1.00\n",
+      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    798.81      1.00\n",
+      " coefs[39]     -0.05      0.09     -0.05     -0.20      0.09    945.47      1.00\n",
+      " coefs[40]      0.08      0.05      0.08     -0.00      0.16    775.94      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.68      0.02   5087.86      1.00\n",
+      " coefs[42]      0.02      0.42      0.03     -0.65      0.71    610.24      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.36      0.40    613.65      1.00\n",
+      " coefs[44]      0.16      0.22      0.16     -0.19      0.52    615.17      1.00\n",
+      " coefs[45]      0.04      0.30      0.05     -0.46      0.52    611.35      1.00\n",
+      " coefs[46]      0.18      0.28      0.19     -0.27      0.65    618.14      1.00\n",
+      " coefs[47]     -0.86      0.56     -0.74     -1.70     -0.08   4596.20      1.00\n",
+      " coefs[48]     -0.08      0.06     -0.08     -0.19      0.02    670.20      1.00\n",
+      " coefs[49]      0.03      1.00      0.04     -1.57      1.71  11583.95      1.00\n",
+      " coefs[50]     -0.87      0.57     -0.76     -1.69     -0.08   4887.46      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.14     -0.41      0.14    618.30      1.00\n",
+      " coefs[52]     -0.19      0.16     -0.19     -0.45      0.08    619.52      1.00\n",
+      " coefs[53]     -0.19      0.13     -0.18     -0.40      0.02    624.71      1.00\n",
+      " coefs[54]     -1.69      0.19     -1.68     -1.99     -1.39   4128.48      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 20 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.89      0.06      1.89      1.79      1.99   9246.42      1.00\n",
+      "  coefs[1]     -0.08      0.03     -0.08     -0.13     -0.02  11208.54      1.00\n",
+      "  coefs[2]      0.01      0.06      0.01     -0.09      0.11   3502.44      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7328.68      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   7942.68      1.00\n",
+      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11139.29      1.00\n",
+      "  coefs[6]      0.47      0.24      0.45      0.07      0.84   2645.70      1.00\n",
+      "  coefs[7]     -0.73      0.15     -0.73     -0.97     -0.49   2807.38      1.00\n",
+      "  coefs[8]      0.85      0.28      0.83      0.40      1.30   2626.09      1.00\n",
+      "  coefs[9]     -0.04      0.03     -0.04     -0.09      0.01  12620.86      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.73      1.44   2934.75      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.51      0.45   2942.71      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.95      1.21   2939.57      1.00\n",
+      " coefs[13]     -0.97      0.64     -0.91     -1.94      0.13   4606.51      1.00\n",
+      " coefs[14]     -0.46      0.66     -0.35     -1.52      0.51   5983.50      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.07   3909.10      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.62      0.11   5133.14      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.26     -0.65      0.09    826.22      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5573.30      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.56      0.56   5610.96      1.00\n",
+      " coefs[20]      0.02      0.97      0.02     -1.57      1.63  10854.73      1.00\n",
+      " coefs[21]      0.01      0.03      0.01     -0.04      0.06    980.00      1.00\n",
+      " coefs[22]      0.05      0.06      0.05     -0.04      0.15    642.18      1.01\n",
+      " coefs[23]      0.01      0.25      0.01     -0.39      0.44    445.60      1.01\n",
+      " coefs[24]     -0.04      0.16     -0.04     -0.30      0.23    464.65      1.01\n",
+      " coefs[25]     -0.07      0.23     -0.07     -0.46      0.32    422.35      1.01\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    425.48      1.01\n",
+      " coefs[27]     -0.70      0.61     -0.59     -1.58      0.16   5206.67      1.00\n",
+      " coefs[28]      0.03      0.99      0.04     -1.55      1.70  10690.05      1.00\n",
+      " coefs[29]      0.11      0.08      0.11     -0.02      0.23    447.83      1.01\n",
+      " coefs[30]     -0.01      0.10     -0.01     -0.18      0.15    609.85      1.01\n",
+      " coefs[31]      0.03      0.08      0.03     -0.10      0.15    668.65      1.00\n",
+      " coefs[32]      0.10      0.09      0.10     -0.05      0.25    435.76      1.01\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.39    423.61      1.01\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.77   4889.49      1.00\n",
+      " coefs[35]      0.35      0.24      0.35     -0.05      0.76    416.61      1.01\n",
+      " coefs[36]      0.32      0.31      0.32     -0.17      0.87    414.14      1.01\n",
+      " coefs[37]      0.18      0.20      0.18     -0.15      0.50    415.80      1.01\n",
+      " coefs[38]     -0.04      0.05     -0.04     -0.12      0.04    964.69      1.00\n",
+      " coefs[39]     -0.03      0.08     -0.02     -0.17      0.10    572.20      1.01\n",
+      " coefs[40]      0.07      0.05      0.07     -0.02      0.15    548.93      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   4809.95      1.00\n",
+      " coefs[42]      0.10      0.42      0.10     -0.55      0.84    414.43      1.01\n",
+      " coefs[43]      0.00      0.23      0.01     -0.36      0.42    420.25      1.01\n",
+      " coefs[44]      0.18      0.22      0.19     -0.18      0.53    414.59      1.01\n",
+      " coefs[45]      0.13      0.30      0.13     -0.35      0.65    412.93      1.01\n",
+      " coefs[46]      0.22      0.28      0.22     -0.25      0.68    414.62      1.01\n",
+      " coefs[47]     -0.12      0.09     -0.12     -0.27      0.01    846.25      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.18      0.02    450.84      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.69     -1.64     -0.00   5076.40      1.00\n",
+      " coefs[50]     -0.83      0.58     -0.70     -1.66     -0.04   4703.44      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.37      0.19    420.59      1.01\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    421.82      1.01\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    430.31      1.01\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   3704.67      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 21 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.90      2.10   9762.19      1.00\n",
+      "  coefs[1]     -0.15      0.04     -0.15     -0.21     -0.09  11181.90      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.21      0.03   3538.15      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.31     -0.21   7643.43      1.00\n",
+      "  coefs[4]     -0.11      0.03     -0.11     -0.16     -0.05   8365.70      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10974.91      1.00\n",
+      "  coefs[6]      0.16      0.29      0.16     -0.31      0.64   2862.26      1.00\n",
+      "  coefs[7]     -0.60      0.18     -0.60     -0.90     -0.32   2967.20      1.00\n",
+      "  coefs[8]      0.53      0.34      0.52     -0.03      1.09   2843.52      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11309.82      1.00\n",
+      " coefs[10]      0.41      0.65      0.40     -0.67      1.47   3281.18      1.00\n",
+      " coefs[11]      0.01      0.29      0.01     -0.48      0.47   3284.19      1.00\n",
+      " coefs[12]      0.09      0.65      0.09     -0.96      1.18   3281.82      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.00     -0.03   4929.61      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.51      0.55   6576.05      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.66      0.04   4629.92      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5257.19      1.00\n",
+      " coefs[17]     -0.06      0.17     -0.06     -0.35      0.21    740.58      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.44   5842.99      1.00\n",
+      " coefs[19]     -0.43      0.67     -0.34     -1.50      0.63   5996.43      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.62      0.02   5050.51      1.00\n",
+      " coefs[21]     -0.77      0.60     -0.66     -1.63      0.04   4806.38      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    781.54      1.00\n",
+      " coefs[23]      0.14      0.24      0.14     -0.25      0.54    588.58      1.00\n",
+      " coefs[24]      0.05      0.15      0.05     -0.21      0.30    592.89      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.12     -0.49      0.26    569.03      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.26      0.32    570.36      1.00\n",
+      " coefs[27]     -0.70      0.62     -0.58     -1.59      0.18   5348.57      1.00\n",
+      " coefs[28]      0.03      0.99      0.02     -1.56      1.72  10094.24      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.04      0.21    603.97      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.12      0.19    749.44      1.00\n",
+      " coefs[31]     -0.00      0.08      0.00     -0.13      0.13    924.25      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.07      0.22    588.87      1.00\n",
+      " coefs[33]      0.10      0.13      0.10     -0.11      0.31    568.07      1.00\n",
+      " coefs[34]      0.14      0.06      0.14      0.04      0.24   1356.03      1.00\n",
+      " coefs[35]      0.28      0.24      0.28     -0.09      0.69    556.98      1.00\n",
+      " coefs[36]      0.31      0.31      0.31     -0.18      0.82    553.33      1.00\n",
+      " coefs[37]      0.17      0.19      0.17     -0.14      0.49    559.88      1.00\n",
+      " coefs[38]      0.01      0.03      0.01     -0.04      0.07    757.07      1.00\n",
+      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    647.92      1.00\n",
+      " coefs[40]      0.04      0.05      0.04     -0.04      0.12    641.85      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1297.18      1.00\n",
+      " coefs[42]      0.00      0.41      0.00     -0.64      0.69    553.97      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.40    559.55      1.00\n",
+      " coefs[44]      0.19      0.21      0.20     -0.15      0.54    560.54      1.00\n",
+      " coefs[45]      0.08      0.29      0.08     -0.39      0.56    556.92      1.00\n",
+      " coefs[46]      0.24      0.28      0.24     -0.18      0.72    555.62      1.00\n",
+      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    894.80      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    627.40      1.00\n",
+      " coefs[49]      0.04      1.01      0.03     -1.59      1.70  10909.59      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.09   4571.07      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.41      0.13    561.78      1.00\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.39      0.12    562.22      1.00\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.37      0.05    562.71      1.00\n",
+      " coefs[54]     -1.66      0.18     -1.65     -1.96     -1.38   4130.36      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 22 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.94      2.15   8792.94      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11601.13      1.00\n",
+      "  coefs[2]     -0.16      0.07     -0.16     -0.27     -0.05   4312.41      1.00\n",
+      "  coefs[3]     -0.32      0.03     -0.32     -0.37     -0.26   6939.66      1.00\n",
+      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.05   7411.87      1.00\n",
+      "  coefs[5]     -0.15      0.03     -0.15     -0.20     -0.10  10025.50      1.00\n",
+      "  coefs[6]     -0.04      0.25     -0.04     -0.45      0.37   3331.37      1.00\n",
+      "  coefs[7]     -0.57      0.15     -0.57     -0.82     -0.32   3563.81      1.00\n",
+      "  coefs[8]      0.29      0.29      0.29     -0.18      0.78   3339.59      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.00      0.09  10370.34      1.00\n",
+      " coefs[10]      0.39      0.66      0.39     -0.69      1.46   3233.84      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.42   3237.79      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -1.03      1.12   3237.01      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   4483.64      1.00\n",
+      " coefs[14]     -0.47      0.67     -0.36     -1.52      0.52   5759.36      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.65      0.04   4528.41      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.60      0.14   4801.30      1.00\n",
+      " coefs[17]     -0.07      0.17     -0.07     -0.35      0.22    832.85      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.42     -1.57      0.40   5510.81      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5378.76      1.00\n",
+      " coefs[20]      0.02      0.98      0.02     -1.59      1.66  12635.21      1.00\n",
+      " coefs[21]      0.00      0.03      0.00     -0.05      0.05   1578.97      1.00\n",
+      " coefs[22]      0.07      0.06      0.07     -0.03      0.15    799.11      1.00\n",
+      " coefs[23]      0.08      0.25      0.08     -0.32      0.50    631.44      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.24      0.28    665.12      1.00\n",
+      " coefs[25]     -0.16      0.23     -0.16     -0.52      0.25    629.61      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.33    649.75      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.12   4951.62      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.63      1.60   9968.12      1.00\n",
+      " coefs[29]      0.04      0.08      0.04     -0.09      0.17    691.13      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.10      0.20    752.47      1.00\n",
+      " coefs[31]      0.01      0.08      0.02     -0.12      0.14   1127.34      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    667.50      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.07      0.37    635.17      1.00\n",
+      " coefs[34]      0.14      0.06      0.14      0.04      0.25   1416.76      1.00\n",
+      " coefs[35]      0.33      0.25      0.33     -0.09      0.72    623.44      1.00\n",
+      " coefs[36]      0.34      0.32      0.34     -0.16      0.87    612.20      1.00\n",
+      " coefs[37]      0.15      0.20      0.15     -0.19      0.46    622.84      1.00\n",
+      " coefs[38]     -0.05      0.05     -0.05     -0.13      0.03   1609.92      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    723.00      1.00\n",
+      " coefs[40]      0.09      0.05      0.09      0.00      0.17    829.79      1.00\n",
+      " coefs[41]      0.03      0.05      0.03     -0.05      0.12    884.95      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.64      0.73    619.81      1.00\n",
+      " coefs[43]     -0.03      0.24     -0.02     -0.43      0.34    621.58      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    617.23      1.00\n",
+      " coefs[45]      0.09      0.30      0.09     -0.39      0.60    618.28      1.00\n",
+      " coefs[46]      0.22      0.28      0.23     -0.23      0.69    608.95      1.00\n",
+      " coefs[47]     -0.02      0.06     -0.02     -0.13      0.08    790.25      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.21      0.00    689.44      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.70     -1.67      0.00   4347.16      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.08   4436.04      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.13     -0.41      0.15    622.46      1.00\n",
+      " coefs[52]     -0.14      0.16     -0.14     -0.41      0.12    634.06      1.00\n",
+      " coefs[53]     -0.11      0.13     -0.11     -0.32      0.11    641.85      1.00\n",
+      " coefs[54]     -1.65      0.18     -1.63     -1.93     -1.33   3934.98      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 23 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.93      0.06      1.93      1.83      2.03   9689.88      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.10      0.01  12545.20      1.00\n",
+      "  coefs[2]     -0.02      0.07     -0.02     -0.13      0.09   3898.07      1.00\n",
+      "  coefs[3]     -0.27      0.03     -0.27     -0.32     -0.21   7686.11      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   8700.67      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.23     -0.13  10401.49      1.00\n",
+      "  coefs[6]      0.26      0.25      0.25     -0.14      0.68   2980.05      1.00\n",
+      "  coefs[7]     -0.67      0.15     -0.67     -0.92     -0.42   3112.42      1.00\n",
+      "  coefs[8]      0.57      0.29      0.56      0.11      1.07   2948.98      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  12414.78      1.00\n",
+      " coefs[10]      0.44      0.65      0.43     -0.63      1.52   2846.10      1.00\n",
+      " coefs[11]     -0.01      0.29     -0.02     -0.51      0.45   2871.59      1.00\n",
+      " coefs[12]      0.10      0.65      0.10     -0.98      1.17   2857.64      1.00\n",
+      " coefs[13]     -1.09      0.63     -1.03     -2.05     -0.01   4990.59      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.36     -1.50      0.54   6165.47      1.00\n",
+      " coefs[15]     -0.81      0.57     -0.71     -1.69      0.02   5048.22      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.08   4824.68      1.00\n",
+      " coefs[17]     -0.16      0.19     -0.15     -0.48      0.13    848.87      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.56      0.40   5827.61      1.00\n",
+      " coefs[19]     -0.45      0.67     -0.36     -1.53      0.58   6544.98      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.65     -1.61      0.04   5423.70      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1947.02      1.00\n",
+      " coefs[22]      0.03      0.06      0.03     -0.06      0.13    874.06      1.00\n",
+      " coefs[23]      0.07      0.24      0.07     -0.32      0.47    585.54      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.23    603.12      1.00\n",
+      " coefs[25]     -0.07      0.23     -0.08     -0.44      0.32    562.41      1.00\n",
+      " coefs[26]     -0.00      0.18     -0.00     -0.28      0.31    574.26      1.00\n",
+      " coefs[27]     -0.62      0.64     -0.50     -1.58      0.31   5547.06      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.58      1.68  10670.31      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.04      0.21    627.27      1.00\n",
+      " coefs[30]      0.01      0.09      0.01     -0.15      0.16    741.73      1.00\n",
+      " coefs[31]     -0.00      0.08      0.00     -0.12      0.13    840.86      1.00\n",
+      " coefs[32]      0.07      0.09      0.06     -0.08      0.21    588.23      1.00\n",
+      " coefs[33]      0.17      0.13      0.16     -0.04      0.39    570.20      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.10      1.77   5030.01      1.00\n",
+      " coefs[35]      0.31      0.24      0.31     -0.08      0.70    559.22      1.00\n",
+      " coefs[36]      0.30      0.31      0.29     -0.20      0.82    552.54      1.00\n",
+      " coefs[37]      0.15      0.19      0.14     -0.17      0.47    551.24      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.08      0.05   1035.24      1.00\n",
+      " coefs[39]     -0.00      0.08     -0.00     -0.13      0.12    664.01      1.00\n",
+      " coefs[40]     -0.01      0.05     -0.01     -0.09      0.07    667.57      1.00\n",
+      " coefs[41]     -0.03      0.07     -0.02     -0.13      0.09   1390.68      1.00\n",
+      " coefs[42]      0.02      0.41      0.01     -0.65      0.69    555.94      1.00\n",
+      " coefs[43]     -0.03      0.23     -0.03     -0.42      0.33    561.70      1.00\n",
+      " coefs[44]      0.16      0.21      0.15     -0.18      0.51    561.34      1.00\n",
+      " coefs[45]      0.06      0.30      0.06     -0.43      0.54    558.07      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.27      0.63    558.31      1.00\n",
+      " coefs[47]     -0.10      0.09     -0.10     -0.23      0.05   1359.88      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.19      0.01    608.20      1.00\n",
+      " coefs[49]      0.03      1.00      0.02     -1.51      1.75  12878.55      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.07   4962.08      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.38      0.16    577.83      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.35      0.17    562.72      1.00\n",
+      " coefs[53]     -0.11      0.13     -0.11     -0.31      0.10    564.13      1.00\n",
+      " coefs[54]     -1.61      0.18     -1.60     -1.89     -1.29   4385.25      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 24 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.07      0.06      2.07      1.97      2.18   9888.07      1.00\n",
+      "  coefs[1]     -0.04      0.04     -0.04     -0.10      0.02  10935.57      1.00\n",
+      "  coefs[2]     -0.22      0.07     -0.22     -0.34     -0.10   3416.86      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   8028.48      1.00\n",
+      "  coefs[4]     -0.12      0.04     -0.12     -0.18     -0.06   8680.12      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.08  11561.50      1.00\n",
+      "  coefs[6]     -0.11      0.29     -0.11     -0.60      0.36   2742.04      1.00\n",
+      "  coefs[7]     -0.47      0.18     -0.47     -0.76     -0.17   2872.73      1.00\n",
+      "  coefs[8]      0.11      0.34      0.11     -0.46      0.65   2724.86      1.00\n",
+      "  coefs[9]     -0.05      0.03     -0.05     -0.10      0.00  11593.39      1.00\n",
+      " coefs[10]      0.46      0.65      0.45     -0.61      1.52   3002.02      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3004.38      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -0.97      1.17   2999.89      1.00\n",
+      " coefs[13]     -1.05      0.62     -0.99     -2.05     -0.03   4368.86      1.00\n",
+      " coefs[14]     -0.46      0.68     -0.34     -1.53      0.53   5985.35      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.70      0.01   4554.68      1.00\n",
+      " coefs[16]     -0.71      0.60     -0.60     -1.63      0.13   5072.77      1.00\n",
+      " coefs[17]      0.08      0.16      0.08     -0.17      0.35    613.24      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.57      0.41   5692.96      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.37     -1.57      0.59   5682.49      1.00\n",
+      " coefs[20]     -0.78      0.58     -0.67     -1.61      0.01   4910.05      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1340.87      1.00\n",
+      " coefs[22]     -0.00      0.07      0.00     -0.12      0.11   1151.16      1.00\n",
+      " coefs[23]      0.19      0.25      0.19     -0.20      0.61    571.15      1.00\n",
+      " coefs[24]      0.07      0.15      0.07     -0.18      0.32    570.76      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.12     -0.52      0.25    570.00      1.00\n",
+      " coefs[26]      0.06      0.18      0.06     -0.24      0.36    570.92      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.14   4857.10      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.63      1.63  11053.83      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.10      0.15    601.17      1.00\n",
+      " coefs[30]      0.08      0.09      0.08     -0.07      0.22    653.46      1.00\n",
+      " coefs[31]      0.02      0.07      0.02     -0.10      0.14    780.03      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.20    587.20      1.00\n",
+      " coefs[33]      0.11      0.13      0.11     -0.10      0.33    578.82      1.00\n",
+      " coefs[34]      0.91      0.59      0.78      0.09      1.76   4633.63      1.00\n",
+      " coefs[35]      0.32      0.24      0.32     -0.10      0.70    562.55      1.00\n",
+      " coefs[36]      0.24      0.31      0.24     -0.25      0.78    550.52      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    553.24      1.00\n",
+      " coefs[38]     -0.06      0.04     -0.06     -0.12      0.00    887.46      1.00\n",
+      " coefs[39]      0.04      0.08      0.04     -0.08      0.17    641.10      1.00\n",
+      " coefs[40]      0.09      0.05      0.08      0.00      0.16    677.50      1.00\n",
+      " coefs[41]      0.03      0.05      0.03     -0.06      0.12    940.91      1.00\n",
+      " coefs[42]     -0.06      0.42     -0.06     -0.71      0.66    556.19      1.00\n",
+      " coefs[43]     -0.06      0.23     -0.06     -0.44      0.33    559.39      1.00\n",
+      " coefs[44]      0.14      0.21      0.14     -0.21      0.50    553.46      1.00\n",
+      " coefs[45]      0.07      0.30      0.07     -0.43      0.56    553.47      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.25      0.68    554.58      1.00\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    783.37      1.00\n",
+      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    604.14      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.68     -1.69     -0.01   4306.68      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   4711.24      1.00\n",
+      " coefs[51]     -0.16      0.17     -0.16     -0.43      0.13    568.23      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.15    568.33      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    579.79      1.00\n",
+      " coefs[54]     -1.60      0.18     -1.58     -1.89     -1.30   3802.32      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 25 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.91      2.12  10309.61      1.00\n",
+      "  coefs[1]     -0.03      0.03     -0.03     -0.09      0.03  12124.19      1.00\n",
+      "  coefs[2]     -0.06      0.07     -0.06     -0.18      0.05   3571.48      1.00\n",
+      "  coefs[3]     -0.28      0.03     -0.28     -0.33     -0.22   7482.98      1.00\n",
+      "  coefs[4]     -0.14      0.04     -0.14     -0.20     -0.08   8459.79      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.10  10634.42      1.00\n",
+      "  coefs[6]      0.38      0.27      0.38     -0.08      0.82   2778.57      1.00\n",
+      "  coefs[7]     -0.76      0.17     -0.76     -1.02     -0.47   2903.10      1.00\n",
+      "  coefs[8]      0.74      0.32      0.74      0.20      1.26   2757.86      1.00\n",
+      "  coefs[9]      0.02      0.03      0.02     -0.03      0.07  12221.01      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.69      1.46   3052.96      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.53      0.42   3052.24      1.00\n",
+      " coefs[12]      0.13      0.65      0.12     -0.94      1.21   3059.80      1.00\n",
+      " coefs[13]     -1.04      0.62     -0.98     -2.09     -0.09   4412.03      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.53      0.53   5862.03      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.65      0.05   5014.93      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.58      0.17   5030.84      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.25     -0.61      0.13   1177.44      1.00\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.54      0.43   5614.50      1.00\n",
+      " coefs[19]     -0.43      0.68     -0.34     -1.54      0.61   5929.27      1.00\n",
+      " coefs[20]      0.02      0.97      0.01     -1.48      1.69  12485.30      1.00\n",
+      " coefs[21]     -0.00      0.03      0.00     -0.05      0.05   1268.53      1.00\n",
+      " coefs[22]      0.06      0.05      0.06     -0.03      0.15    729.52      1.00\n",
+      " coefs[23]      0.19      0.25      0.19     -0.24      0.57    558.82      1.00\n",
+      " coefs[24]      0.05      0.16      0.05     -0.21      0.31    580.78      1.00\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.50      0.27    548.09      1.00\n",
+      " coefs[26]      0.09      0.18      0.09     -0.22      0.38    547.89      1.00\n",
+      " coefs[27]     -0.70      0.61     -0.58     -1.60      0.15   5096.35      1.00\n",
+      " coefs[28]      0.02      0.99      0.02     -1.66      1.61  10390.05      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    580.62      1.00\n",
+      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    628.19      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.62      0.07   4801.85      1.00\n",
+      " coefs[32]      0.09      0.09      0.09     -0.05      0.24    565.21      1.00\n",
+      " coefs[33]      0.15      0.13      0.16     -0.06      0.37    550.40      1.00\n",
+      " coefs[34]      0.09      0.05      0.09      0.01      0.18    895.13      1.00\n",
+      " coefs[35]      0.33      0.24      0.34     -0.07      0.74    535.96      1.00\n",
+      " coefs[36]      0.32      0.31      0.33     -0.19      0.84    533.22      1.00\n",
+      " coefs[37]      0.14      0.20      0.14     -0.20      0.45    537.09      1.00\n",
+      " coefs[38]     -0.02      0.04     -0.02     -0.09      0.04    939.95      1.00\n",
+      " coefs[39]      0.00      0.08      0.00     -0.12      0.13    647.96      1.00\n",
+      " coefs[40]      0.09      0.06      0.09      0.00      0.18    799.91      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1291.14      1.00\n",
+      " coefs[42]      0.07      0.42      0.08     -0.62      0.77    533.62      1.00\n",
+      " coefs[43]     -0.02      0.23     -0.01     -0.40      0.37    534.58      1.00\n",
+      " coefs[44]      0.16      0.22      0.17     -0.20      0.51    534.54      1.00\n",
+      " coefs[45]      0.09      0.30      0.10     -0.41      0.58    533.79      1.00\n",
+      " coefs[46]      0.22      0.28      0.23     -0.26      0.66    535.06      1.00\n",
+      " coefs[47]     -0.08      0.07     -0.08     -0.20      0.03    832.04      1.00\n",
+      " coefs[48]     -0.04      0.06     -0.04     -0.15      0.06    617.55      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.01   4879.90      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.73     -1.68     -0.08   4615.40      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.13     -0.43      0.13    546.89      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.38      0.16    536.48      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.18     -0.40      0.03    552.97      1.00\n",
+      " coefs[54]     -1.76      0.19     -1.75     -2.06     -1.45   3911.71      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 26 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.95      0.06      1.95      1.85      2.05   9697.28      1.00\n",
+      "  coefs[1]     -0.01      0.03     -0.01     -0.07      0.04  12200.46      1.00\n",
+      "  coefs[2]     -0.18      0.07     -0.18     -0.28     -0.07   3835.72      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.36     -0.25   7753.40      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8914.41      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13   9799.48      1.00\n",
+      "  coefs[6]     -0.44      0.25     -0.44     -0.83     -0.02   3083.93      1.00\n",
+      "  coefs[7]     -0.24      0.15     -0.24     -0.48      0.01   3272.49      1.00\n",
+      "  coefs[8]     -0.25      0.29     -0.24     -0.73      0.22   3069.29      1.00\n",
+      "  coefs[9]     -0.01      0.03     -0.01     -0.06      0.04  11351.99      1.00\n",
+      " coefs[10]      0.42      0.65      0.41     -0.72      1.42   3244.67      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.50      0.46   3259.76      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -1.05      1.09   3243.82      1.00\n",
+      " coefs[13]     -1.10      0.62     -1.04     -2.07     -0.06   4756.45      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.52   5832.99      1.00\n",
+      " coefs[15]     -0.81      0.57     -0.70     -1.65      0.03   4664.33      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.63      0.09   5437.49      1.00\n",
+      " coefs[17]     -0.01      0.17     -0.01     -0.27      0.27    593.91      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   5946.46      1.00\n",
+      " coefs[19]     -0.45      0.69     -0.35     -1.53      0.63   5809.86      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   4961.15      1.00\n",
+      " coefs[21]     -0.77      0.58     -0.65     -1.61      0.02   5202.46      1.00\n",
+      " coefs[22]      0.05      0.05      0.05     -0.03      0.15    658.39      1.00\n",
+      " coefs[23]      0.17      0.25      0.17     -0.23      0.58    514.11      1.00\n",
+      " coefs[24]      0.08      0.16      0.08     -0.17      0.34    523.59      1.00\n",
+      " coefs[25]     -0.08      0.24     -0.08     -0.46      0.32    507.06      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    507.58      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.60     -1.61      0.13   4905.48      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.60      1.69  10750.90      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    555.98      1.00\n",
+      " coefs[30]      0.01      0.10      0.01     -0.15      0.17    672.45      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.12      0.13    807.56      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.09      0.21    533.46      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.07      0.38    508.16      1.00\n",
+      " coefs[34]      0.93      0.60      0.80      0.11      1.79   4631.74      1.00\n",
+      " coefs[35]      0.30      0.24      0.30     -0.08      0.73    494.20      1.00\n",
+      " coefs[36]      0.34      0.31      0.34     -0.15      0.88    494.83      1.00\n",
+      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    497.12      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.03      0.11    896.21      1.00\n",
+      " coefs[39]     -0.01      0.08     -0.00     -0.14      0.12    622.27      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.01      0.15    578.36      1.00\n",
+      " coefs[41]     -0.78      0.58     -0.66     -1.63      0.03   5017.98      1.00\n",
+      " coefs[42]      0.08      0.42      0.08     -0.62      0.76    493.89      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.34      0.43    499.52      1.00\n",
+      " coefs[44]      0.13      0.22      0.13     -0.21      0.50    496.38      1.00\n",
+      " coefs[45]      0.08      0.30      0.08     -0.44      0.56    492.93      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.28      0.65    498.64      1.00\n",
+      " coefs[47]     -0.82      0.57     -0.71     -1.67     -0.05   4656.06      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.04    550.33      1.00\n",
+      " coefs[49]     -0.80      0.59     -0.67     -1.65     -0.00   4704.70      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.07   4427.45      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.17    502.20      1.00\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.35      0.18    502.02      1.00\n",
+      " coefs[53]     -0.16      0.13     -0.16     -0.38      0.05    512.18      1.00\n",
+      " coefs[54]     -1.68      0.19     -1.66     -1.96     -1.36   3876.22      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 27 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09   9664.80      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.11      0.00  12273.76      1.00\n",
+      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3990.60      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   8378.52      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   9122.81      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11   9835.89      1.00\n",
+      "  coefs[6]      0.43      0.28      0.43     -0.05      0.88   3212.70      1.00\n",
+      "  coefs[7]     -0.79      0.17     -0.79     -1.08     -0.52   3328.05      1.00\n",
+      "  coefs[8]      0.87      0.33      0.86      0.31      1.40   3201.38      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  12410.57      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.68      1.46   3077.07      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.56      0.40   3088.73      1.00\n",
+      " coefs[12]      0.11      0.65      0.10     -0.94      1.19   3080.15      1.00\n",
+      " coefs[13]     -1.00      0.63     -0.93     -2.05     -0.02   4853.41      1.00\n",
+      " coefs[14]     -0.44      0.67     -0.33     -1.47      0.59   5749.68      1.00\n",
+      " coefs[15]     -0.76      0.57     -0.66     -1.64      0.06   4580.98      1.00\n",
+      " coefs[16]     -0.74      0.58     -0.63     -1.59      0.11   4965.06      1.00\n",
+      " coefs[17]      0.08      0.16      0.08     -0.20      0.33    757.62      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.55      0.42   5849.73      1.00\n",
+      " coefs[19]     -0.45      0.66     -0.36     -1.51      0.59   6230.51      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.61      0.03   4981.49      1.00\n",
+      " coefs[21]      0.03      0.02      0.03     -0.01      0.07   1097.70      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.05      0.14    997.56      1.00\n",
+      " coefs[23]      0.11      0.25      0.11     -0.31      0.51    703.71      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.27      0.25    725.63      1.00\n",
+      " coefs[25]     -0.05      0.23     -0.05     -0.44      0.32    685.14      1.00\n",
+      " coefs[26]      0.04      0.18      0.04     -0.26      0.33    689.06      1.00\n",
+      " coefs[27]     -0.70      0.63     -0.58     -1.63      0.17   4768.90      1.00\n",
+      " coefs[28]      0.02      1.00      0.03     -1.60      1.70  11348.00      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.11      0.15    782.70      1.00\n",
+      " coefs[30]      0.00      0.10      0.00     -0.17      0.17   1066.32      1.00\n",
+      " coefs[31]     -0.75      0.58     -0.63     -1.61      0.07   4989.76      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    711.07      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    689.21      1.00\n",
+      " coefs[34]      0.15      0.06      0.15      0.04      0.25   1520.05      1.00\n",
+      " coefs[35]      0.35      0.24      0.35     -0.05      0.75    671.45      1.00\n",
+      " coefs[36]      0.37      0.31      0.38     -0.15      0.87    674.78      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.49    677.33      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    942.01      1.00\n",
+      " coefs[39]     -0.07      0.09     -0.06     -0.21      0.07   1046.12      1.00\n",
+      " coefs[40]      0.05      0.05      0.06     -0.03      0.14    837.95      1.00\n",
+      " coefs[41]     -0.79      0.59     -0.66     -1.65      0.04   5069.57      1.00\n",
+      " coefs[42]      0.09      0.42      0.09     -0.60      0.76    671.11      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.37      0.40    680.37      1.00\n",
+      " coefs[44]      0.17      0.21      0.18     -0.18      0.53    673.74      1.00\n",
+      " coefs[45]      0.12      0.30      0.13     -0.35      0.64    669.63      1.00\n",
+      " coefs[46]      0.25      0.28      0.25     -0.19      0.73    674.48      1.00\n",
+      " coefs[47]     -0.84      0.58     -0.71     -1.70     -0.04   4818.66      1.00\n",
+      " coefs[48]     -0.05      0.06     -0.05     -0.16      0.05    730.24      1.00\n",
+      " coefs[49]     -0.80      0.60     -0.68     -1.65      0.02   4871.11      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.73     -1.68     -0.08   4482.28      1.00\n",
+      " coefs[51]     -0.10      0.17     -0.10     -0.38      0.17    679.51      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.12     -0.39      0.13    679.23      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.08    691.74      1.00\n",
+      " coefs[54]     -1.77      0.19     -1.76     -2.05     -1.45   4110.31      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 28 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.06      0.06      2.06      1.95      2.16  10589.43      1.00\n",
+      "  coefs[1]     -0.01      0.04     -0.01     -0.07      0.05  12371.89      1.00\n",
+      "  coefs[2]     -0.00      0.07     -0.00     -0.12      0.12   3405.65      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   8382.81      1.00\n",
+      "  coefs[4]     -0.10      0.03     -0.10     -0.16     -0.05   9570.33      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.22     -0.11  11024.17      1.00\n",
+      "  coefs[6]      0.43      0.29      0.43     -0.05      0.92   2818.87      1.00\n",
+      "  coefs[7]     -0.81      0.18     -0.80     -1.10     -0.52   2976.70      1.00\n",
+      "  coefs[8]      0.78      0.34      0.77      0.23      1.36   2826.32      1.00\n",
+      "  coefs[9]      0.01      0.03      0.01     -0.04      0.06  11133.18      1.00\n",
+      " coefs[10]      0.46      0.65      0.46     -0.62      1.50   3195.00      1.00\n",
+      " coefs[11]     -0.09      0.29     -0.09     -0.56      0.39   3191.49      1.00\n",
+      " coefs[12]      0.07      0.65      0.06     -0.99      1.13   3197.02      1.00\n",
+      " coefs[13]     -0.99      0.63     -0.93     -2.01      0.02   5157.05      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.50      0.55   6122.62      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.63      0.08   4822.13      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.60      0.12   5059.19      1.00\n",
+      " coefs[17]     -0.10      0.19     -0.09     -0.41      0.20    945.77      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.56      0.41   5737.00      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.54      0.60   5933.46      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.62      0.02   4978.14      1.00\n",
+      " coefs[21]      0.03      0.03      0.03     -0.02      0.07   1257.64      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.05      0.13    949.70      1.00\n",
+      " coefs[23]      0.08      0.24      0.09     -0.31      0.49    632.12      1.00\n",
+      " coefs[24]     -0.02      0.16     -0.02     -0.28      0.24    651.47      1.00\n",
+      " coefs[25]     -0.11      0.23     -0.10     -0.48      0.27    596.53      1.00\n",
+      " coefs[26]      0.04      0.18      0.04     -0.26      0.32    596.33      1.00\n",
+      " coefs[27]     -0.73      0.62     -0.60     -1.63      0.14   5089.50      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.63      1.64  10446.30      1.00\n",
+      " coefs[29]      0.02      0.08      0.02     -0.11      0.14    685.01      1.00\n",
+      " coefs[30]      0.01      0.10      0.01     -0.16      0.17    939.40      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.17      0.13   1350.65      1.00\n",
+      " coefs[32]      0.05      0.09      0.05     -0.09      0.20    622.62      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.05      0.38    604.88      1.00\n",
+      " coefs[34]      0.14      0.06      0.13      0.04      0.24   1503.83      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.06      0.72    589.40      1.00\n",
+      " coefs[36]      0.32      0.31      0.33     -0.18      0.83    582.35      1.00\n",
+      " coefs[37]      0.14      0.19      0.15     -0.17      0.46    591.16      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04    968.98      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    743.97      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.06      0.11    730.94      1.00\n",
+      " coefs[41]     -0.80      0.58     -0.68     -1.68     -0.02   5204.80      1.00\n",
+      " coefs[42]      0.01      0.41      0.02     -0.67      0.66    584.43      1.00\n",
+      " coefs[43]     -0.07      0.23     -0.07     -0.44      0.30    588.94      1.00\n",
+      " coefs[44]      0.17      0.21      0.17     -0.18      0.51    582.84      1.00\n",
+      " coefs[45]      0.17      0.29      0.18     -0.32      0.64    585.86      1.00\n",
+      " coefs[46]      0.23      0.27      0.23     -0.25      0.65    586.24      1.00\n",
+      " coefs[47]     -0.12      0.09     -0.11     -0.26      0.02   1237.70      1.00\n",
+      " coefs[48]     -0.09      0.06     -0.09     -0.18      0.02    645.34      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.03   1713.26      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.68     -0.07   4466.26      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.11     -0.38      0.16    596.53      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    593.47      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.19     -0.41      0.00    611.55      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.41   4242.11      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 29 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.99      0.06      1.99      1.89      2.09  10281.72      1.00\n",
+      "  coefs[1]     -0.08      0.03     -0.08     -0.14     -0.02  11111.60      1.00\n",
+      "  coefs[2]     -0.11      0.08     -0.11     -0.24      0.02   3283.15      1.00\n",
+      "  coefs[3]     -0.29      0.03     -0.29     -0.34     -0.23   7208.35      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.03   8500.50      1.00\n",
+      "  coefs[5]     -0.10      0.03     -0.10     -0.16     -0.05  11522.62      1.00\n",
+      "  coefs[6]     -0.03      0.33     -0.03     -0.58      0.52   2779.03      1.00\n",
+      "  coefs[7]     -0.49      0.20     -0.49     -0.83     -0.17   2911.34      1.00\n",
+      "  coefs[8]      0.24      0.39      0.24     -0.44      0.85   2776.23      1.00\n",
+      "  coefs[9]     -0.07      0.03     -0.07     -0.11     -0.02  10734.26      1.00\n",
+      " coefs[10]      0.41      0.65      0.41     -0.67      1.45   3176.70      1.00\n",
+      " coefs[11]     -0.03      0.29     -0.03     -0.51      0.44   3179.52      1.00\n",
+      " coefs[12]      0.10      0.65      0.09     -0.97      1.16   3177.55      1.00\n",
+      " coefs[13]     -1.00      0.64     -0.94     -2.00      0.02   4659.78      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.54   5589.40      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.70     -1.67      0.03   4418.25      1.00\n",
+      " coefs[16]     -0.72      0.59     -0.60     -1.61      0.12   5208.44      1.00\n",
+      " coefs[17]     -0.17      0.19     -0.16     -0.47      0.15    943.32      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.45     -1.58      0.39   5903.46      1.00\n",
+      " coefs[19]     -0.47      0.69     -0.38     -1.55      0.61   5385.20      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.63      0.02   5011.82      1.00\n",
+      " coefs[21]      0.04      0.03      0.04     -0.01      0.09   1530.86      1.00\n",
+      " coefs[22]      0.09      0.05      0.09      0.00      0.17    733.93      1.00\n",
+      " coefs[23]      0.04      0.25      0.04     -0.37      0.44    635.37      1.00\n",
+      " coefs[24]     -0.00      0.16     -0.01     -0.27      0.25    647.37      1.00\n",
+      " coefs[25]     -0.14      0.23     -0.14     -0.51      0.26    626.98      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.28      0.32    634.01      1.00\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.61      0.16   4950.71      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.58      1.65  10491.51      1.00\n",
+      " coefs[29]      0.08      0.08      0.08     -0.06      0.20    667.60      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.11      0.19    785.86      1.00\n",
+      " coefs[31]      0.04      0.07      0.05     -0.07      0.17    933.56      1.00\n",
+      " coefs[32]      0.07      0.09      0.07     -0.08      0.21    650.23      1.00\n",
+      " coefs[33]      0.20      0.13      0.20     -0.01      0.43    626.70      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.11      1.77   4818.61      1.00\n",
+      " coefs[35]      0.31      0.24      0.30     -0.10      0.70    609.88      1.00\n",
+      " coefs[36]      0.31      0.31      0.31     -0.21      0.82    613.54      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.16      0.48    621.85      1.00\n",
+      " coefs[38]     -0.02      0.05     -0.02     -0.11      0.06   1553.81      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.13    739.41      1.00\n",
+      " coefs[40]      0.10      0.05      0.10      0.01      0.19    890.30      1.00\n",
+      " coefs[41]     -0.01      0.07     -0.00     -0.12      0.10   1456.92      1.00\n",
+      " coefs[42]      0.02      0.42      0.01     -0.67      0.69    613.09      1.00\n",
+      " coefs[43]     -0.00      0.23     -0.01     -0.40      0.37    621.98      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.21      0.50    614.00      1.00\n",
+      " coefs[45]      0.07      0.30      0.07     -0.43      0.55    621.21      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.26      0.66    620.99      1.00\n",
+      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00   1359.24      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    644.79      1.00\n",
+      " coefs[49]     -0.82      0.60     -0.70     -1.68     -0.01   4763.74      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.72     -1.69     -0.06   4904.38      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.15    629.04      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.34      0.18    630.19      1.00\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.03    631.24      1.00\n",
+      " coefs[54]     -1.64      0.19     -1.62     -1.93     -1.34   3831.89      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 30 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.90      0.06      1.90      1.80      2.00   9019.97      1.00\n",
+      "  coefs[1]     -0.04      0.03     -0.04     -0.10      0.02  10767.61      1.00\n",
+      "  coefs[2]      0.02      0.07      0.02     -0.10      0.14   3295.95      1.00\n",
+      "  coefs[3]     -0.26      0.03     -0.26     -0.32     -0.21   7375.50      1.00\n",
+      "  coefs[4]     -0.08      0.04     -0.08     -0.14     -0.02   8457.63      1.00\n",
+      "  coefs[5]     -0.14      0.03     -0.14     -0.19     -0.09  10886.68      1.00\n",
+      "  coefs[6]      0.50      0.29      0.50      0.03      0.97   2663.40      1.00\n",
+      "  coefs[7]     -0.78      0.18     -0.78     -1.08     -0.50   2793.04      1.00\n",
+      "  coefs[8]      0.88      0.34      0.88      0.30      1.41   2672.27      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.07      0.02  10751.40      1.00\n",
+      " coefs[10]      0.42      0.65      0.41     -0.61      1.51   3393.24      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.48      0.47   3406.03      1.00\n",
+      " coefs[12]      0.07      0.65      0.07     -0.99      1.13   3403.50      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.05     -0.03   4984.38      1.00\n",
+      " coefs[14]     -0.46      0.66     -0.36     -1.47      0.53   5921.21      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.64      0.05   4545.78      1.00\n",
+      " coefs[16]     -0.73      0.57     -0.61     -1.58      0.10   5089.11      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17   1126.41      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.44     -1.55      0.41   5515.73      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.57      0.56   5501.46      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.61      0.03   5123.43      1.00\n",
+      " coefs[21]     -0.76      0.59     -0.64     -1.61      0.05   4825.12      1.00\n",
+      " coefs[22]      0.02      0.07      0.03     -0.10      0.14   1548.35      1.00\n",
+      " coefs[23]      0.05      0.25      0.06     -0.35      0.47    783.10      1.00\n",
+      " coefs[24]      0.08      0.16      0.09     -0.16      0.35    779.21      1.00\n",
+      " coefs[25]     -0.10      0.23     -0.09     -0.49      0.28    756.44      1.00\n",
+      " coefs[26]     -0.00      0.18      0.00     -0.29      0.31    755.12      1.00\n",
+      " coefs[27]     -0.71      0.63     -0.58     -1.63      0.17   4745.70      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.54      1.73   9981.61      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    854.92      1.00\n",
+      " coefs[30]     -0.09      0.13     -0.08     -0.28      0.13   1528.49      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.64     -1.61      0.07   4759.95      1.00\n",
+      " coefs[32]      0.13      0.09      0.13     -0.02      0.27    775.07      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.05      0.39    764.75      1.00\n",
+      " coefs[34]      0.91      0.60      0.79      0.08      1.76   4523.52      1.00\n",
+      " coefs[35]      0.37      0.24      0.37     -0.02      0.79    745.02      1.01\n",
+      " coefs[36]      0.35      0.31      0.35     -0.13      0.90    743.92      1.00\n",
+      " coefs[37]      0.19      0.20      0.20     -0.13      0.52    747.52      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.02     -0.09      0.04   1238.03      1.00\n",
+      " coefs[39]      0.01      0.08      0.02     -0.11      0.14    874.10      1.00\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    917.48      1.00\n",
+      " coefs[41]      0.01      0.05      0.01     -0.08      0.10   1128.55      1.00\n",
+      " coefs[42]      0.05      0.41      0.05     -0.64      0.74    740.73      1.00\n",
+      " coefs[43]     -0.04      0.23     -0.04     -0.41      0.36    744.09      1.00\n",
+      " coefs[44]      0.18      0.21      0.18     -0.16      0.55    748.09      1.00\n",
+      " coefs[45]      0.15      0.30      0.16     -0.32      0.67    742.57      1.00\n",
+      " coefs[46]      0.21      0.28      0.22     -0.24      0.68    748.05      1.00\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05   1192.87      1.00\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    845.74      1.00\n",
+      " coefs[49]     -0.79      0.60     -0.68     -1.65      0.01   5087.76      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.72     -1.69     -0.05   4519.70      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.08     -0.37      0.19    749.63      1.00\n",
+      " coefs[52]     -0.09      0.16     -0.09     -0.38      0.15    752.57      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.36      0.07    766.61      1.00\n",
+      " coefs[54]     -1.70      0.19     -1.69     -2.00     -1.40   4002.84      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 31 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.00      0.06      2.00      1.89      2.10  10506.43      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.02     -0.08      0.04  11576.31      1.00\n",
+      "  coefs[2]     -0.09      0.07     -0.09     -0.20      0.03   3713.76      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.42     -0.31   8843.21      1.00\n",
+      "  coefs[4]     -0.05      0.04     -0.05     -0.10      0.01   9500.03      1.00\n",
+      "  coefs[5]     -0.09      0.03     -0.09     -0.14     -0.04  10864.35      1.00\n",
+      "  coefs[6]      0.33      0.27      0.32     -0.10      0.76   2852.16      1.00\n",
+      "  coefs[7]     -0.76      0.16     -0.75     -1.01     -0.48   2964.01      1.00\n",
+      "  coefs[8]      0.69      0.31      0.68      0.19      1.20   2847.07      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11519.52      1.00\n",
+      " coefs[10]      0.39      0.65      0.39     -0.70      1.46   3245.63      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3261.90      1.00\n",
+      " coefs[12]      0.11      0.65      0.11     -0.92      1.23   3256.33      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.95     -2.04     -0.03   5056.56      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.49      0.54   6112.69      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.60      0.08   4585.07      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.61     -1.61      0.11   5040.88      1.00\n",
+      " coefs[17]     -0.26      0.23     -0.25     -0.62      0.12   1111.71      1.00\n",
+      " coefs[18]     -0.54      0.66     -0.42     -1.56      0.42   5994.44      1.00\n",
+      " coefs[19]     -0.45      0.67     -0.35     -1.57      0.57   5768.92      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.01   5062.81      1.00\n",
+      " coefs[21]     -0.77      0.59     -0.65     -1.61      0.02   5297.12      1.00\n",
+      " coefs[22]      0.06      0.06      0.06     -0.04      0.16    832.32      1.00\n",
+      " coefs[23]      0.14      0.25      0.14     -0.27      0.54    553.00      1.01\n",
+      " coefs[24]      0.09      0.16      0.09     -0.18      0.33    554.02      1.01\n",
+      " coefs[25]     -0.12      0.24     -0.12     -0.51      0.26    538.13      1.01\n",
+      " coefs[26]      0.03      0.18      0.03     -0.28      0.32    545.03      1.01\n",
+      " coefs[27]     -0.68      0.63     -0.56     -1.63      0.18   4961.27      1.00\n",
+      " coefs[28]      0.03      0.99      0.03     -1.62      1.65  10677.03      1.00\n",
+      " coefs[29]      0.09      0.08      0.09     -0.04      0.22    593.65      1.01\n",
+      " coefs[30]      0.07      0.09      0.07     -0.08      0.21    650.49      1.01\n",
+      " coefs[31]     -0.02      0.10     -0.02     -0.18      0.13   1189.70      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    571.81      1.01\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.38    540.11      1.01\n",
+      " coefs[34]      0.15      0.07      0.14      0.04      0.25   1289.56      1.00\n",
+      " coefs[35]      0.35      0.25      0.35     -0.06      0.74    528.74      1.01\n",
+      " coefs[36]      0.31      0.31      0.31     -0.22      0.81    527.93      1.01\n",
+      " coefs[37]      0.15      0.20      0.15     -0.18      0.47    535.58      1.01\n",
+      " coefs[38]     -0.82      0.58     -0.69     -1.66     -0.03   5038.93      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    632.38      1.01\n",
+      " coefs[40]      0.07      0.05      0.07     -0.01      0.15    644.97      1.01\n",
+      " coefs[41]     -0.79      0.59     -0.67     -1.66      0.03   4898.98      1.00\n",
+      " coefs[42]      0.04      0.42      0.05     -0.68      0.69    530.13      1.01\n",
+      " coefs[43]      0.00      0.23      0.01     -0.38      0.38    535.88      1.01\n",
+      " coefs[44]      0.18      0.22      0.18     -0.19      0.52    531.17      1.01\n",
+      " coefs[45]      0.11      0.30      0.11     -0.39      0.60    527.06      1.01\n",
+      " coefs[46]      0.26      0.28      0.26     -0.21      0.71    527.83      1.01\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.15      0.07    742.72      1.01\n",
+      " coefs[48]     -0.07      0.06     -0.07     -0.17      0.03    592.25      1.01\n",
+      " coefs[49]     -0.80      0.59     -0.68     -1.65      0.01   4900.71      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.75     -1.71     -0.09   4640.27      1.00\n",
+      " coefs[51]     -0.11      0.17     -0.11     -0.40      0.16    539.58      1.01\n",
+      " coefs[52]     -0.10      0.16     -0.10     -0.38      0.15    540.36      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.38      0.04    553.93      1.01\n",
+      " coefs[54]     -1.79      0.19     -1.77     -2.09     -1.49   4183.29      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 32 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.04      0.06      2.04      1.93      2.14  10125.47      1.00\n",
+      "  coefs[1]     -0.03      0.04     -0.03     -0.09      0.03  11574.62      1.00\n",
+      "  coefs[2]     -0.05      0.08     -0.05     -0.17      0.08   3281.43      1.00\n",
+      "  coefs[3]     -0.35      0.03     -0.35     -0.41     -0.29   7593.31      1.00\n",
+      "  coefs[4]     -0.07      0.04     -0.07     -0.13     -0.01   8084.89      1.00\n",
+      "  coefs[5]     -0.13      0.03     -0.13     -0.19     -0.08  10905.67      1.00\n",
+      "  coefs[6]     -0.31      0.31     -0.30     -0.82      0.18   2706.12      1.00\n",
+      "  coefs[7]     -0.31      0.19     -0.31     -0.64     -0.02   2873.98      1.00\n",
+      "  coefs[8]     -0.05      0.36     -0.04     -0.64      0.54   2711.99      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.01  11662.00      1.00\n",
+      " coefs[10]      0.36      0.65      0.35     -0.70      1.45   3104.82      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.55      0.40   3113.43      1.00\n",
+      " coefs[12]      0.13      0.65      0.11     -0.91      1.23   3110.90      1.00\n",
+      " coefs[13]     -0.92      0.65     -0.85     -1.98      0.10   4557.60      1.00\n",
+      " coefs[14]     -0.48      0.67     -0.37     -1.53      0.52   5472.45      1.00\n",
+      " coefs[15]     -0.77      0.57     -0.67     -1.66      0.05   4497.69      1.00\n",
+      " coefs[16]     -0.75      0.58     -0.64     -1.60      0.10   5133.58      1.00\n",
+      " coefs[17]     -0.19      0.19     -0.18     -0.49      0.11    650.98      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.45     -1.58      0.38   5533.20      1.00\n",
+      " coefs[19]     -0.48      0.68     -0.39     -1.60      0.56   5797.66      1.00\n",
+      " coefs[20]     -0.77      0.58     -0.65     -1.62      0.02   5225.53      1.00\n",
+      " coefs[21]      0.85      0.59      0.73      0.05      1.69   4743.33      1.00\n",
+      " coefs[22]      0.08      0.06      0.08     -0.01      0.17    616.41      1.00\n",
+      " coefs[23]     -0.12      0.26     -0.12     -0.55      0.27    509.35      1.00\n",
+      " coefs[24]      0.01      0.16      0.01     -0.26      0.26    505.07      1.00\n",
+      " coefs[25]     -0.06      0.23     -0.06     -0.46      0.31    470.64      1.00\n",
+      " coefs[26]     -0.01      0.18     -0.01     -0.32      0.28    466.27      1.00\n",
+      " coefs[27]     -0.73      0.61     -0.61     -1.62      0.11   4885.26      1.00\n",
+      " coefs[28]      0.02      1.00      0.03     -1.53      1.77  10588.75      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.07      0.18    499.21      1.00\n",
+      " coefs[30]      0.00      0.10      0.00     -0.16      0.17    651.77      1.00\n",
+      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13    974.28      1.00\n",
+      " coefs[32]      0.13      0.09      0.13     -0.02      0.28    487.05      1.00\n",
+      " coefs[33]      0.16      0.13      0.16     -0.06      0.37    456.31      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.78   4689.58      1.00\n",
+      " coefs[35]      0.36      0.24      0.36     -0.03      0.77    458.75      1.00\n",
+      " coefs[36]      0.36      0.31      0.36     -0.15      0.86    453.29      1.00\n",
+      " coefs[37]      0.13      0.20      0.13     -0.18      0.46    457.34      1.00\n",
+      " coefs[38]      0.00      0.05      0.01     -0.08      0.09   1270.06      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    528.49      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    533.76      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.02     -0.13      0.09   1041.39      1.00\n",
+      " coefs[42]      0.09      0.42      0.08     -0.61      0.74    455.70      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.35      0.40    460.85      1.00\n",
+      " coefs[44]      0.14      0.22      0.15     -0.22      0.49    447.48      1.00\n",
+      " coefs[45]      0.10      0.30      0.10     -0.39      0.58    452.15      1.00\n",
+      " coefs[46]      0.17      0.28      0.17     -0.28      0.63    450.76      1.00\n",
+      " coefs[47]     -0.14      0.09     -0.13     -0.28      0.00    959.11      1.00\n",
+      " coefs[48]     -0.04      0.06     -0.04     -0.14      0.07    493.15      1.00\n",
+      " coefs[49]     -0.81      0.59     -0.69     -1.65     -0.01   4845.43      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.07   4590.09      1.00\n",
+      " coefs[51]     -0.14      0.17     -0.15     -0.43      0.12    466.09      1.00\n",
+      " coefs[52]     -0.11      0.16     -0.11     -0.37      0.15    465.86      1.00\n",
+      " coefs[53]     -0.13      0.13     -0.13     -0.34      0.08    473.04      1.00\n",
+      " coefs[54]     -1.67      0.19     -1.66     -1.97     -1.36   4072.51      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 33 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.91      0.06      1.91      1.81      2.01  10511.47      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12220.55      1.00\n",
+      "  coefs[2]     -0.07      0.07     -0.07     -0.19      0.04   3687.76      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   7665.75      1.00\n",
+      "  coefs[4]     -0.06      0.03     -0.06     -0.11     -0.00   9077.63      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.18     -0.07  11684.74      1.00\n",
+      "  coefs[6]      0.26      0.29      0.25     -0.20      0.75   2923.46      1.00\n",
+      "  coefs[7]     -0.61      0.18     -0.61     -0.89     -0.31   3050.64      1.00\n",
+      "  coefs[8]      0.61      0.34      0.60      0.07      1.20   2919.52      1.00\n",
+      "  coefs[9]     -0.03      0.03     -0.03     -0.08      0.02  11351.45      1.00\n",
+      " coefs[10]      0.39      0.65      0.38     -0.73      1.41   3228.80      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.04     -0.54      0.41   3241.45      1.00\n",
+      " coefs[12]      0.11      0.64      0.11     -1.00      1.13   3238.02      1.00\n",
+      " coefs[13]     -0.97      0.64     -0.91     -1.98      0.07   5249.99      1.00\n",
+      " coefs[14]     -0.47      0.66     -0.37     -1.48      0.54   6066.89      1.00\n",
+      " coefs[15]     -0.77      0.56     -0.67     -1.64      0.04   4986.07      1.00\n",
+      " coefs[16]     -0.73      0.58     -0.62     -1.61      0.09   5444.07      1.00\n",
+      " coefs[17]     -0.14      0.19     -0.14     -0.44      0.17    776.12      1.00\n",
+      " coefs[18]     -0.53      0.67     -0.42     -1.55      0.44   6209.21      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.39     -1.57      0.55   6230.36      1.00\n",
+      " coefs[20]     -0.78      0.59     -0.66     -1.62      0.02   5067.27      1.00\n",
+      " coefs[21]     -0.76      0.58     -0.65     -1.59      0.05   5458.41      1.00\n",
+      " coefs[22]     -0.00      0.07      0.00     -0.12      0.12   1121.18      1.00\n",
+      " coefs[23]      0.03      0.25      0.04     -0.37      0.44    541.73      1.00\n",
+      " coefs[24]      0.02      0.16      0.02     -0.24      0.27    539.71      1.00\n",
+      " coefs[25]     -0.05      0.23     -0.06     -0.43      0.33    515.63      1.00\n",
+      " coefs[26]      0.05      0.18      0.05     -0.24      0.35    517.55      1.00\n",
+      " coefs[27]     -0.72      0.61     -0.59     -1.60      0.15   5250.27      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.58      1.68  11408.51      1.00\n",
+      " coefs[29]      0.10      0.08      0.10     -0.03      0.22    537.16      1.00\n",
+      " coefs[30]      0.03      0.09      0.04     -0.11      0.18    614.05      1.00\n",
+      " coefs[31]     -0.03      0.10     -0.02     -0.18      0.13   1169.25      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    546.97      1.00\n",
+      " coefs[33]      0.17      0.13      0.17     -0.04      0.39    519.49      1.00\n",
+      " coefs[34]      0.92      0.59      0.80      0.11      1.76   4777.97      1.00\n",
+      " coefs[35]      0.37      0.25      0.37     -0.01      0.78    501.98      1.00\n",
+      " coefs[36]      0.36      0.31      0.36     -0.17      0.85    498.97      1.00\n",
+      " coefs[37]      0.20      0.20      0.20     -0.13      0.51    509.05      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.04    846.24      1.00\n",
+      " coefs[39]     -0.02      0.08     -0.02     -0.14      0.12    639.66      1.00\n",
+      " coefs[40]      0.02      0.05      0.02     -0.06      0.10    608.38      1.00\n",
+      " coefs[41]     -0.80      0.59     -0.68     -1.66      0.01   4980.95      1.00\n",
+      " coefs[42]      0.09      0.42      0.09     -0.57      0.79    505.92      1.00\n",
+      " coefs[43]      0.01      0.23      0.00     -0.37      0.39    510.07      1.00\n",
+      " coefs[44]      0.17      0.22      0.17     -0.17      0.53    501.53      1.00\n",
+      " coefs[45]      0.08      0.30      0.08     -0.42      0.56    499.88      1.00\n",
+      " coefs[46]      0.19      0.28      0.19     -0.29      0.62    505.21      1.00\n",
+      " coefs[47]     -0.86      0.57     -0.74     -1.70     -0.06   4649.67      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.04    529.40      1.00\n",
+      " coefs[49]      0.04      1.00      0.02     -1.59      1.66  12157.87      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.73     -1.71     -0.08   4732.51      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.40      0.16    504.47      1.00\n",
+      " coefs[52]     -0.08      0.16     -0.08     -0.33      0.19    511.03      1.00\n",
+      " coefs[53]     -0.14      0.13     -0.14     -0.35      0.07    515.84      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.70     -2.01     -1.40   4097.08      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 34 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.05      0.06      2.05      1.95      2.16  10000.30      1.00\n",
+      "  coefs[1]     -0.02      0.04     -0.01     -0.07      0.05  10626.97      1.00\n",
+      "  coefs[2]     -0.14      0.07     -0.14     -0.26     -0.02   3772.39      1.00\n",
+      "  coefs[3]     -0.36      0.03     -0.36     -0.41     -0.30   7420.44      1.00\n",
+      "  coefs[4]     -0.05      0.03     -0.05     -0.11      0.01   8047.09      1.00\n",
+      "  coefs[5]     -0.19      0.03     -0.19     -0.24     -0.13  10672.51      1.00\n",
+      "  coefs[6]     -0.17      0.28     -0.17     -0.63      0.30   3074.31      1.00\n",
+      "  coefs[7]     -0.40      0.17     -0.40     -0.69     -0.13   3264.91      1.00\n",
+      "  coefs[8]      0.07      0.33      0.07     -0.46      0.63   3067.33      1.00\n",
+      "  coefs[9]      0.00      0.03      0.00     -0.05      0.05  11678.49      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.61      1.54   3198.32      1.00\n",
+      " coefs[11]     -0.06      0.29     -0.06     -0.57      0.39   3220.36      1.00\n",
+      " coefs[12]      0.08      0.65      0.08     -1.01      1.14   3215.87      1.00\n",
+      " coefs[13]     -1.07      0.62     -1.01     -2.06     -0.07   4551.88      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.35     -1.51      0.54   6254.49      1.00\n",
+      " coefs[15]     -0.80      0.57     -0.69     -1.63      0.06   4416.51      1.00\n",
+      " coefs[16]     -0.71      0.59     -0.60     -1.60      0.13   4831.45      1.00\n",
+      " coefs[17]      0.01      0.17      0.01     -0.26      0.28    591.23      1.00\n",
+      " coefs[18]     -0.55      0.66     -0.43     -1.55      0.42   6005.73      1.00\n",
+      " coefs[19]     -0.45      0.69     -0.36     -1.53      0.63   5509.96      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.66     -1.61      0.02   5084.54      1.00\n",
+      " coefs[21]      0.05      0.03      0.04     -0.01      0.10   1382.99      1.00\n",
+      " coefs[22]      0.10      0.05      0.10      0.02      0.19    596.70      1.00\n",
+      " coefs[23]      0.12      0.25      0.12     -0.30      0.51    508.75      1.00\n",
+      " coefs[24]      0.03      0.16      0.03     -0.23      0.28    514.96      1.00\n",
+      " coefs[25]     -0.10      0.24     -0.11     -0.49      0.27    492.31      1.00\n",
+      " coefs[26]      0.02      0.18      0.02     -0.27      0.32    498.67      1.00\n",
+      " coefs[27]     -0.71      0.61     -0.60     -1.61      0.13   4956.76      1.00\n",
+      " coefs[28]      0.01      0.99      0.01     -1.54      1.69  11010.12      1.00\n",
+      " coefs[29]      0.05      0.08      0.05     -0.08      0.18    556.65      1.00\n",
+      " coefs[30]      0.09      0.09      0.10     -0.05      0.24    614.00      1.00\n",
+      " coefs[31]      0.01      0.08      0.01     -0.12      0.14    795.57      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    512.23      1.00\n",
+      " coefs[33]      0.13      0.13      0.13     -0.09      0.35    502.30      1.00\n",
+      " coefs[34]      0.91      0.59      0.80      0.12      1.77   4902.15      1.00\n",
+      " coefs[35]      0.30      0.25      0.29     -0.11      0.70    491.25      1.00\n",
+      " coefs[36]      0.32      0.32      0.32     -0.20      0.82    483.51      1.00\n",
+      " coefs[37]      0.16      0.20      0.16     -0.17      0.47    490.31      1.00\n",
+      " coefs[38]     -0.03      0.04     -0.03     -0.09      0.03    803.24      1.00\n",
+      " coefs[39]      0.02      0.08      0.02     -0.10      0.15    590.41      1.00\n",
+      " coefs[40]      0.06      0.05      0.06     -0.02      0.14    588.34      1.00\n",
+      " coefs[41]      0.01      0.07      0.01     -0.10      0.12   1292.79      1.00\n",
+      " coefs[42]     -0.02      0.42     -0.02     -0.71      0.65    487.70      1.00\n",
+      " coefs[43]     -0.03      0.23     -0.04     -0.42      0.34    497.84      1.00\n",
+      " coefs[44]      0.15      0.22      0.15     -0.20      0.51    490.22      1.00\n",
+      " coefs[45]      0.10      0.30      0.10     -0.39      0.60    486.10      1.00\n",
+      " coefs[46]      0.20      0.28      0.20     -0.27      0.64    490.41      1.00\n",
+      " coefs[47]     -0.86      0.56     -0.75     -1.70     -0.08   4880.99      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.16      0.05    543.91      1.00\n",
+      " coefs[49]     -0.81      0.60     -0.70     -1.66      0.01   4856.94      1.00\n",
+      " coefs[50]     -0.84      0.59     -0.72     -1.70     -0.06   4479.77      1.00\n",
+      " coefs[51]     -0.15      0.17     -0.15     -0.43      0.12    499.77      1.00\n",
+      " coefs[52]     -0.12      0.16     -0.13     -0.38      0.14    497.92      1.00\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    497.46      1.00\n",
+      " coefs[54]     -1.64      0.18     -1.62     -1.92     -1.33   3835.59      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 35 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.97      1.87      2.07   9742.14      1.00\n",
+      "  coefs[1]     -0.06      0.04     -0.06     -0.12     -0.00  10941.17      1.00\n",
+      "  coefs[2]     -0.15      0.07     -0.15     -0.27     -0.04   3797.76      1.00\n",
+      "  coefs[3]     -0.37      0.03     -0.37     -0.42     -0.31   7795.70      1.00\n",
+      "  coefs[4]     -0.03      0.03     -0.03     -0.09      0.03   8579.09      1.00\n",
+      "  coefs[5]     -0.18      0.03     -0.18     -0.24     -0.13  10418.88      1.00\n",
+      "  coefs[6]      0.05      0.28      0.05     -0.39      0.52   2999.81      1.00\n",
+      "  coefs[7]     -0.57      0.17     -0.57     -0.85     -0.29   3099.11      1.00\n",
+      "  coefs[8]      0.46      0.33      0.46     -0.08      0.99   3002.13      1.00\n",
+      "  coefs[9]     -0.08      0.03     -0.08     -0.13     -0.03  10895.90      1.00\n",
+      " coefs[10]      0.47      0.64      0.48     -0.58      1.53   3303.11      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.49      0.44   3312.49      1.00\n",
+      " coefs[12]      0.07      0.64      0.07     -1.00      1.10   3315.68      1.00\n",
+      " coefs[13]     -1.07      0.61     -1.00     -2.06     -0.09   4977.49      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.45      0.58   5820.49      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.67     -1.65      0.06   4544.59      1.00\n",
+      " coefs[16]     -0.72      0.58     -0.60     -1.59      0.10   4799.76      1.00\n",
+      " coefs[17]      0.03      0.16      0.04     -0.24      0.30    739.13      1.01\n",
+      " coefs[18]     -0.53      0.66     -0.41     -1.58      0.40   6011.13      1.00\n",
+      " coefs[19]     -0.47      0.68     -0.37     -1.59      0.56   5503.24      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.63      0.02   4644.05      1.00\n",
+      " coefs[21]     -0.78      0.58     -0.66     -1.63      0.01   4745.88      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.01      0.17    873.25      1.01\n",
+      " coefs[23]      0.09      0.25      0.09     -0.31      0.51    688.44      1.01\n",
+      " coefs[24]      0.03      0.16      0.03     -0.22      0.30    737.69      1.01\n",
+      " coefs[25]     -0.05      0.23     -0.04     -0.42      0.36    662.47      1.01\n",
+      " coefs[26]      0.05      0.18      0.06     -0.24      0.36    675.97      1.01\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.61      0.11   4795.73      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.61      1.69  10020.48      1.00\n",
+      " coefs[29]      0.07      0.08      0.07     -0.06      0.20    720.56      1.01\n",
+      " coefs[30]      0.05      0.09      0.05     -0.10      0.20    833.72      1.01\n",
+      " coefs[31]      0.02      0.08      0.02     -0.11      0.15   1020.81      1.00\n",
+      " coefs[32]      0.06      0.09      0.06     -0.08      0.21    684.55      1.01\n",
+      " coefs[33]      0.14      0.13      0.14     -0.07      0.36    677.90      1.01\n",
+      " coefs[34]      0.13      0.06      0.12      0.03      0.23   1738.80      1.00\n",
+      " coefs[35]      0.28      0.24      0.29     -0.13      0.67    646.54      1.01\n",
+      " coefs[36]      0.28      0.31      0.29     -0.23      0.81    657.65      1.01\n",
+      " coefs[37]      0.21      0.20      0.21     -0.11      0.54    652.29      1.01\n",
+      " coefs[38]      0.01      0.03      0.01     -0.05      0.07    862.31      1.01\n",
+      " coefs[39]     -0.02      0.08     -0.02     -0.15      0.12    869.75      1.01\n",
+      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    755.29      1.01\n",
+      " coefs[41]      0.03      0.05      0.03     -0.06      0.12   1142.51      1.00\n",
+      " coefs[42]     -0.00      0.42      0.00     -0.67      0.72    652.36      1.01\n",
+      " coefs[43]     -0.02      0.23     -0.02     -0.41      0.36    663.81      1.01\n",
+      " coefs[44]      0.14      0.22      0.14     -0.22      0.50    651.86      1.01\n",
+      " coefs[45]      0.07      0.30      0.07     -0.44      0.56    654.79      1.01\n",
+      " coefs[46]      0.19      0.28      0.20     -0.25      0.68    656.43      1.01\n",
+      " coefs[47]     -0.07      0.07     -0.07     -0.19      0.05    993.49      1.00\n",
+      " coefs[48]     -0.11      0.06     -0.11     -0.22     -0.01    734.51      1.01\n",
+      " coefs[49]     -0.79      0.60     -0.67     -1.64      0.03   4950.47      1.00\n",
+      " coefs[50]     -0.87      0.58     -0.74     -1.69     -0.08   4526.96      1.00\n",
+      " coefs[51]     -0.13      0.17     -0.13     -0.41      0.15    668.74      1.01\n",
+      " coefs[52]     -0.12      0.16     -0.11     -0.38      0.15    669.40      1.01\n",
+      " coefs[53]     -0.20      0.13     -0.20     -0.41      0.02    676.97      1.01\n",
+      " coefs[54]     -1.65      0.18     -1.64     -1.93     -1.34   4116.09      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 36 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.96      0.06      1.96      1.86      2.06   9372.47      1.00\n",
+      "  coefs[1]     -0.05      0.03     -0.05     -0.11      0.00  10822.01      1.00\n",
+      "  coefs[2]     -0.17      0.06     -0.17     -0.27     -0.07   3864.52      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.39     -0.28   7410.99      1.00\n",
+      "  coefs[4]     -0.05      0.03     -0.05     -0.10      0.01   8105.01      1.00\n",
+      "  coefs[5]     -0.12      0.03     -0.12     -0.17     -0.06  10915.47      1.00\n",
+      "  coefs[6]     -0.03      0.22     -0.03     -0.40      0.33   2760.58      1.00\n",
+      "  coefs[7]     -0.48      0.13     -0.48     -0.69     -0.26   3090.19      1.00\n",
+      "  coefs[8]      0.28      0.25      0.27     -0.12      0.72   2820.91      1.00\n",
+      "  coefs[9]     -0.02      0.03     -0.02     -0.07      0.03  11238.51      1.00\n",
+      " coefs[10]      0.40      0.65      0.40     -0.71      1.44   3232.80      1.00\n",
+      " coefs[11]     -0.02      0.29     -0.02     -0.50      0.46   3242.27      1.00\n",
+      " coefs[12]      0.12      0.65      0.11     -0.97      1.18   3245.95      1.00\n",
+      " coefs[13]     -1.05      0.63     -1.00     -2.09     -0.07   5192.61      1.00\n",
+      " coefs[14]     -0.44      0.68     -0.33     -1.49      0.58   5836.55      1.00\n",
+      " coefs[15]     -0.79      0.57     -0.69     -1.65      0.04   4569.53      1.00\n",
+      " coefs[16]     -0.73      0.59     -0.62     -1.65      0.09   5300.47      1.00\n",
+      " coefs[17]     -0.02      0.17     -0.02     -0.29      0.28    807.36      1.01\n",
+      " coefs[18]     -0.56      0.66     -0.44     -1.59      0.38   5962.50      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.38     -1.57      0.57   5232.08      1.00\n",
+      " coefs[20]      0.02      0.98      0.03     -1.59      1.63  12107.78      1.00\n",
+      " coefs[21]     -0.77      0.60     -0.64     -1.63      0.05   4698.56      1.00\n",
+      " coefs[22]      0.08      0.05      0.08     -0.00      0.17    756.90      1.01\n",
+      " coefs[23]      0.11      0.26      0.11     -0.32      0.52    701.29      1.01\n",
+      " coefs[24]      0.06      0.16      0.06     -0.21      0.31    635.73      1.01\n",
+      " coefs[25]     -0.06      0.24     -0.06     -0.48      0.31    644.03      1.01\n",
+      " coefs[26]     -0.01      0.19     -0.01     -0.31      0.30    665.28      1.01\n",
+      " coefs[27]     -0.72      0.61     -0.61     -1.59      0.12   5029.47      1.00\n",
+      " coefs[28]      0.03      1.00      0.02     -1.63      1.65  10008.37      1.00\n",
+      " coefs[29]      0.01      0.08      0.01     -0.12      0.15    712.05      1.01\n",
+      " coefs[30]      0.03      0.09      0.03     -0.12      0.18    801.77      1.01\n",
+      " coefs[31]     -0.05      0.10     -0.05     -0.20      0.11   1444.46      1.01\n",
+      " coefs[32]      0.13      0.09      0.13     -0.03      0.27    721.44      1.01\n",
+      " coefs[33]      0.11      0.14      0.12     -0.12      0.32    656.94      1.01\n",
+      " coefs[34]      0.91      0.60      0.78      0.09      1.79   4477.44      1.00\n",
+      " coefs[35]      0.29      0.25      0.29     -0.14      0.68    652.55      1.01\n",
+      " coefs[36]      0.30      0.32      0.30     -0.27      0.78    645.31      1.01\n",
+      " coefs[37]      0.12      0.20      0.13     -0.22      0.44    649.06      1.01\n",
+      " coefs[38]      0.00      0.03      0.00     -0.06      0.06    814.07      1.01\n",
+      " coefs[39]     -0.01      0.08     -0.01     -0.15      0.13    885.40      1.01\n",
+      " coefs[40]      0.03      0.05      0.03     -0.06      0.11    786.68      1.01\n",
+      " coefs[41]      0.01      0.06      0.01     -0.08      0.10   1079.71      1.01\n",
+      " coefs[42]      0.03      0.43      0.03     -0.71      0.69    657.11      1.01\n",
+      " coefs[43]     -0.04      0.24     -0.04     -0.45      0.34    660.02      1.01\n",
+      " coefs[44]      0.12      0.22      0.12     -0.26      0.46    643.07      1.01\n",
+      " coefs[45]      0.07      0.31      0.08     -0.44      0.56    656.44      1.01\n",
+      " coefs[46]      0.22      0.29      0.22     -0.26      0.68    652.23      1.01\n",
+      " coefs[47]     -0.05      0.07     -0.05     -0.17      0.07   1065.65      1.01\n",
+      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    689.46      1.01\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.67     -0.00   4683.36      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.69     -0.08   4867.74      1.00\n",
+      " coefs[51]     -0.12      0.17     -0.12     -0.41      0.16    682.73      1.01\n",
+      " coefs[52]     -0.14      0.17     -0.14     -0.43      0.11    670.78      1.01\n",
+      " coefs[53]     -0.17      0.13     -0.17     -0.39      0.05    678.49      1.01\n",
+      " coefs[54]     -1.63      0.18     -1.61     -1.92     -1.32   3991.08      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 37 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.12  10190.29      1.00\n",
+      "  coefs[1]      0.03      0.04      0.03     -0.03      0.09  11618.83      1.00\n",
+      "  coefs[2]     -0.08      0.07     -0.08     -0.19      0.04   3901.96      1.00\n",
+      "  coefs[3]     -0.30      0.03     -0.30     -0.35     -0.24   8168.46      1.00\n",
+      "  coefs[4]     -0.06      0.04     -0.06     -0.12     -0.00   9352.54      1.00\n",
+      "  coefs[5]     -0.17      0.03     -0.17     -0.23     -0.12  11575.01      1.00\n",
+      "  coefs[6]      0.44      0.27      0.42     -0.00      0.87   3054.71      1.00\n",
+      "  coefs[7]     -0.85      0.16     -0.84     -1.11     -0.58   3227.23      1.00\n",
+      "  coefs[8]      0.81      0.31      0.80      0.29      1.31   3054.83      1.00\n",
+      "  coefs[9]      0.04      0.03      0.04     -0.01      0.09  11497.32      1.00\n",
+      " coefs[10]      0.43      0.65      0.42     -0.66      1.50   3059.84      1.00\n",
+      " coefs[11]     -0.07      0.29     -0.08     -0.57      0.39   3069.11      1.00\n",
+      " coefs[12]      0.05      0.65      0.04     -1.03      1.12   3065.23      1.00\n",
+      " coefs[13]     -0.95      0.64     -0.89     -1.95      0.10   5155.64      1.00\n",
+      " coefs[14]     -0.45      0.67     -0.34     -1.46      0.60   6013.74      1.00\n",
+      " coefs[15]     -0.76      0.58     -0.65     -1.62      0.10   4813.79      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.58     -1.57      0.16   5147.70      1.00\n",
+      " coefs[17]     -0.85      0.55     -0.76     -1.68     -0.01   4545.60      1.00\n",
+      " coefs[18]     -0.56      0.66     -0.43     -1.54      0.44   6040.82      1.00\n",
+      " coefs[19]     -0.47      0.67     -0.37     -1.57      0.55   6180.31      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.04   5180.47      1.00\n",
+      " coefs[21]     -0.78      0.59     -0.66     -1.62      0.03   5257.24      1.00\n",
+      " coefs[22]      0.04      0.06      0.04     -0.06      0.13    996.95      1.00\n",
+      " coefs[23]      0.05      0.24      0.05     -0.38      0.42    686.43      1.00\n",
+      " coefs[24]      0.14      0.15      0.14     -0.12      0.38    671.57      1.00\n",
+      " coefs[25]     -0.12      0.23     -0.11     -0.49      0.26    670.77      1.00\n",
+      " coefs[26]      0.11      0.18      0.12     -0.18      0.39    661.76      1.00\n",
+      " coefs[27]     -0.70      0.62     -0.59     -1.60      0.17   5031.16      1.00\n",
+      " coefs[28]      0.02      1.00      0.02     -1.63      1.68  10507.75      1.00\n",
+      " coefs[29]      0.03      0.08      0.03     -0.10      0.16    760.67      1.00\n",
+      " coefs[30]      0.10      0.09      0.10     -0.05      0.24    811.00      1.00\n",
+      " coefs[31]     -0.76      0.59     -0.63     -1.60      0.08   4563.06      1.00\n",
+      " coefs[32]      0.11      0.09      0.11     -0.04      0.25    686.24      1.00\n",
+      " coefs[33]      0.18      0.13      0.18     -0.03      0.39    665.40      1.00\n",
+      " coefs[34]      0.93      0.59      0.81      0.13      1.80   4500.21      1.00\n",
+      " coefs[35]      0.39      0.24      0.40     -0.02      0.76    645.92      1.00\n",
+      " coefs[36]      0.43      0.31      0.43     -0.11      0.90    646.61      1.00\n",
+      " coefs[37]      0.20      0.19      0.20     -0.13      0.50    649.74      1.00\n",
+      " coefs[38]      0.04      0.04      0.04     -0.02      0.10    945.88      1.00\n",
+      " coefs[39]      0.04      0.08      0.04     -0.09      0.16    786.82      1.00\n",
+      " coefs[40]      0.12      0.05      0.12      0.03      0.20    849.33      1.00\n",
+      " coefs[41]     -0.78      0.59     -0.65     -1.66      0.03   5036.10      1.00\n",
+      " coefs[42]      0.02      0.41      0.03     -0.70      0.64    646.14      1.00\n",
+      " coefs[43]      0.01      0.23      0.01     -0.39      0.36    650.33      1.00\n",
+      " coefs[44]      0.23      0.21      0.23     -0.16      0.53    641.32      1.00\n",
+      " coefs[45]      0.16      0.29      0.17     -0.35      0.62    645.40      1.00\n",
+      " coefs[46]      0.28      0.27      0.28     -0.20      0.70    644.22      1.00\n",
+      " coefs[47]     -0.04      0.07     -0.04     -0.16      0.07    992.72      1.00\n",
+      " coefs[48]     -0.06      0.06     -0.06     -0.17      0.03    734.82      1.00\n",
+      " coefs[49]     -0.01      0.03     -0.01     -0.05      0.04   1801.99      1.00\n",
+      " coefs[50]     -0.85      0.59     -0.74     -1.69     -0.05   4857.12      1.00\n",
+      " coefs[51]     -0.08      0.17     -0.08     -0.38      0.17    656.17      1.00\n",
+      " coefs[52]     -0.06      0.16     -0.06     -0.34      0.17    660.34      1.00\n",
+      " coefs[53]     -0.15      0.13     -0.15     -0.36      0.05    673.66      1.00\n",
+      " coefs[54]     -1.86      0.20     -1.84     -2.17     -1.51   4098.42      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 38 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.06      1.96      1.87      2.07  10096.48      1.00\n",
+      "  coefs[1]     -0.06      0.03     -0.06     -0.12     -0.01  12244.36      1.00\n",
+      "  coefs[2]     -0.04      0.06     -0.04     -0.15      0.07   4159.98      1.00\n",
+      "  coefs[3]     -0.33      0.03     -0.33     -0.38     -0.27   7749.88      1.00\n",
+      "  coefs[4]     -0.08      0.03     -0.08     -0.14     -0.02   8882.58      1.00\n",
+      "  coefs[5]     -0.11      0.03     -0.11     -0.16     -0.06  11482.48      1.00\n",
+      "  coefs[6]      0.07      0.24      0.06     -0.32      0.47   3120.93      1.00\n",
+      "  coefs[7]     -0.51      0.15     -0.51     -0.75     -0.26   3283.63      1.00\n",
+      "  coefs[8]      0.42      0.28      0.42     -0.05      0.87   3098.35      1.00\n",
+      "  coefs[9]     -0.06      0.03     -0.06     -0.11     -0.01  11951.39      1.00\n",
+      " coefs[10]      0.45      0.65      0.44     -0.62      1.53   3260.72      1.00\n",
+      " coefs[11]     -0.04      0.29     -0.05     -0.56      0.40   3274.76      1.00\n",
+      " coefs[12]      0.06      0.65      0.05     -1.00      1.15   3282.00      1.00\n",
+      " coefs[13]     -1.05      0.62     -1.00     -2.12     -0.12   5389.23      1.00\n",
+      " coefs[14]     -0.46      0.68     -0.35     -1.52      0.56   6658.42      1.00\n",
+      " coefs[15]     -0.79      0.56     -0.69     -1.65      0.05   5438.21      1.00\n",
+      " coefs[16]     -0.70      0.59     -0.59     -1.60      0.15   5338.59      1.00\n",
+      " coefs[17]     -0.27      0.23     -0.25     -0.63      0.11   1265.14      1.00\n",
+      " coefs[18]     -0.57      0.66     -0.46     -1.59      0.38   5781.56      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.36     -1.53      0.61   6188.61      1.00\n",
+      " coefs[20]     -0.76      0.59     -0.64     -1.62      0.04   5486.01      1.00\n",
+      " coefs[21]      0.03      0.04      0.03     -0.03      0.09   1964.40      1.00\n",
+      " coefs[22]      0.01      0.07      0.01     -0.11      0.13   1235.89      1.00\n",
+      " coefs[23]      0.10      0.25      0.10     -0.32      0.49    591.69      1.00\n",
+      " coefs[24]      0.08      0.16      0.08     -0.19      0.32    595.98      1.00\n",
+      " coefs[25]     -0.08      0.23     -0.08     -0.47      0.30    576.69      1.00\n",
+      " coefs[26]      0.03      0.18      0.03     -0.26      0.33    584.84      1.00\n",
+      " coefs[27]     -0.71      0.61     -0.59     -1.60      0.14   5240.14      1.00\n",
+      " coefs[28]      0.03      1.00      0.03     -1.59      1.68  11781.73      1.00\n",
+      " coefs[29]      0.06      0.08      0.07     -0.06      0.19    634.64      1.00\n",
+      " coefs[30]      0.04      0.09      0.04     -0.12      0.18    665.09      1.00\n",
+      " coefs[31]     -0.76      0.58     -0.64     -1.62      0.05   4939.89      1.00\n",
+      " coefs[32]      0.04      0.09      0.04     -0.10      0.19    595.34      1.00\n",
+      " coefs[33]      0.15      0.13      0.15     -0.05      0.38    588.17      1.00\n",
+      " coefs[34]      0.91      0.59      0.79      0.10      1.77   4449.06      1.00\n",
+      " coefs[35]      0.29      0.24      0.30     -0.12      0.68    566.20      1.00\n",
+      " coefs[36]      0.35      0.31      0.35     -0.19      0.84    565.96      1.00\n",
+      " coefs[37]      0.19      0.20      0.19     -0.12      0.52    569.22      1.00\n",
+      " coefs[38]     -0.06      0.04     -0.05     -0.12      0.01    935.97      1.00\n",
+      " coefs[39]      0.01      0.08      0.01     -0.12      0.14    737.66      1.00\n",
+      " coefs[40]      0.05      0.05      0.05     -0.04      0.13    682.67      1.00\n",
+      " coefs[41]     -0.02      0.07     -0.01     -0.12      0.10   1363.24      1.00\n",
+      " coefs[42]      0.05      0.42      0.05     -0.64      0.72    564.74      1.00\n",
+      " coefs[43]      0.03      0.23      0.03     -0.38      0.39    570.94      1.00\n",
+      " coefs[44]      0.18      0.21      0.19     -0.18      0.53    568.55      1.00\n",
+      " coefs[45]      0.15      0.30      0.15     -0.35      0.63    562.05      1.00\n",
+      " coefs[46]      0.23      0.28      0.23     -0.24      0.68    565.69      1.00\n",
+      " coefs[47]     -0.84      0.57     -0.72     -1.69     -0.04   4863.24      1.00\n",
+      " coefs[48]     -0.10      0.06     -0.09     -0.20      0.01    649.56      1.00\n",
+      " coefs[49]      0.03      1.01      0.02     -1.55      1.72  11743.21      1.00\n",
+      " coefs[50]     -0.85      0.58     -0.72     -1.68     -0.06   5084.52      1.00\n",
+      " coefs[51]     -0.09      0.17     -0.09     -0.38      0.18    574.15      1.00\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.41      0.12    576.37      1.00\n",
+      " coefs[53]     -0.18      0.13     -0.17     -0.39      0.03    578.29      1.00\n",
+      " coefs[54]     -1.71      0.19     -1.69     -2.00     -1.38   4122.53      1.00\n",
+      "\n",
+      "\n",
+      "\n",
+      " =============================== SUBPOSTERIOR 39 ===============================\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      2.02      0.06      2.02      1.92      2.13  10022.35      1.00\n",
+      "  coefs[1]     -0.07      0.04     -0.07     -0.13     -0.02  11930.67      1.00\n",
+      "  coefs[2]      0.09      0.07      0.09     -0.03      0.21   3565.47      1.00\n",
+      "  coefs[3]     -0.31      0.03     -0.31     -0.36     -0.25   7874.95      1.00\n",
+      "  coefs[4]     -0.10      0.04     -0.10     -0.16     -0.04   8677.59      1.00\n",
+      "  coefs[5]     -0.16      0.03     -0.16     -0.21     -0.11  11143.46      1.00\n",
+      "  coefs[6]      0.64      0.30      0.63      0.17      1.14   2850.68      1.00\n",
+      "  coefs[7]     -0.90      0.18     -0.89     -1.21     -0.61   3006.07      1.00\n",
+      "  coefs[8]      1.05      0.35      1.04      0.50      1.63   2848.02      1.00\n",
+      "  coefs[9]      0.05      0.03      0.05      0.00      0.10  11434.28      1.00\n",
+      " coefs[10]      0.38      0.65      0.37     -0.73      1.41   3027.13      1.00\n",
+      " coefs[11]     -0.05      0.29     -0.05     -0.56      0.40   3049.82      1.00\n",
+      " coefs[12]      0.14      0.65      0.14     -0.93      1.20   3039.84      1.00\n",
+      " coefs[13]     -1.01      0.63     -0.94     -2.00     -0.00   4993.50      1.00\n",
+      " coefs[14]     -0.46      0.67     -0.35     -1.52      0.53   5614.94      1.00\n",
+      " coefs[15]     -0.78      0.57     -0.68     -1.63      0.06   4675.04      1.00\n",
+      " coefs[16]     -0.70      0.58     -0.59     -1.57      0.15   5153.50      1.00\n",
+      " coefs[17]     -0.05      0.17     -0.04     -0.32      0.23    652.24      1.01\n",
+      " coefs[18]     -0.52      0.66     -0.40     -1.52      0.44   6037.65      1.00\n",
+      " coefs[19]     -0.46      0.68     -0.36     -1.55      0.61   6114.54      1.00\n",
+      " coefs[20]     -0.77      0.59     -0.65     -1.60      0.02   4987.38      1.00\n",
+      " coefs[21]     -0.75      0.59     -0.64     -1.59      0.05   4951.24      1.00\n",
+      " coefs[22]     -0.75      0.60     -0.63     -1.63      0.05   4435.53      1.00\n",
+      " coefs[23]      0.12      0.24      0.12     -0.27      0.51    500.82      1.01\n",
+      " coefs[24]      0.03      0.15      0.03     -0.24      0.26    526.83      1.01\n",
+      " coefs[25]     -0.04      0.23     -0.04     -0.42      0.33    494.40      1.01\n",
+      " coefs[26]      0.01      0.17      0.01     -0.28      0.30    506.35      1.01\n",
+      " coefs[27]     -0.71      0.62     -0.59     -1.59      0.16   5403.79      1.00\n",
+      " coefs[28]      0.02      0.99      0.03     -1.55      1.70  10861.75      1.00\n",
+      " coefs[29]      0.06      0.08      0.06     -0.06      0.19    543.44      1.01\n",
+      " coefs[30]      0.08      0.09      0.08     -0.06      0.22    601.06      1.01\n",
+      " coefs[31]     -0.02      0.09     -0.01     -0.17      0.13   1105.50      1.00\n",
+      " coefs[32]      0.08      0.09      0.08     -0.06      0.23    526.65      1.01\n",
+      " coefs[33]      0.12      0.13      0.12     -0.10      0.32    494.20      1.01\n",
+      " coefs[34]      0.93      0.59      0.81      0.12      1.79   4585.26      1.00\n",
+      " coefs[35]      0.34      0.24      0.34     -0.05      0.72    491.75      1.01\n",
+      " coefs[36]      0.37      0.30      0.37     -0.14      0.86    486.39      1.01\n",
+      " coefs[37]      0.15      0.19      0.15     -0.16      0.47    488.15      1.01\n",
+      " coefs[38]     -0.01      0.03     -0.01     -0.07      0.05    676.92      1.01\n",
+      " coefs[39]      0.05      0.07      0.05     -0.07      0.17    570.31      1.01\n",
+      " coefs[40]      0.02      0.05      0.03     -0.05      0.11    563.75      1.01\n",
+      " coefs[41]     -0.78      0.59     -0.66     -1.63      0.03   4822.95      1.00\n",
+      " coefs[42]      0.05      0.40      0.06     -0.59      0.74    487.94      1.01\n",
+      " coefs[43]      0.01      0.23      0.01     -0.36      0.38    491.71      1.01\n",
+      " coefs[44]      0.19      0.21      0.20     -0.17      0.52    491.92      1.01\n",
+      " coefs[45]      0.07      0.29      0.08     -0.42      0.53    489.32      1.01\n",
+      " coefs[46]      0.20      0.27      0.20     -0.26      0.63    486.73      1.01\n",
+      " coefs[47]     -0.10      0.07     -0.10     -0.21      0.01    773.52      1.01\n",
+      " coefs[48]     -0.12      0.06     -0.12     -0.22     -0.02    540.35      1.01\n",
+      " coefs[49]     -0.81      0.60     -0.69     -1.66     -0.02   4748.32      1.00\n",
+      " coefs[50]     -0.86      0.58     -0.74     -1.70     -0.08   4705.07      1.00\n",
+      " coefs[51]     -0.13      0.16     -0.13     -0.40      0.14    498.31      1.01\n",
+      " coefs[52]     -0.13      0.16     -0.13     -0.38      0.13    504.10      1.01\n",
+      " coefs[53]     -0.15      0.13     -0.14     -0.35      0.06    502.86      1.01\n",
+      " coefs[54]     -1.75      0.19     -1.74     -2.05     -1.45   4340.91      1.00\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(1), K)\n",
+    "subposteriors = []\n",
+    "for i, (rng, shard) in enumerate(zip(rngs, shards)):\n",
+    "    sep = '=' * 31\n",
+    "    print('\\n ' + sep + ' SUBPOSTERIOR {:02d} '.format(i) + sep, end='')\n",
+    "    samples = get_subposterior(rng, shard, K)\n",
+    "    if not os.path.exists('.results'):\n",
+    "        os.makedirs('.results')\n",
+    "    np.save('.results/subposterior_{:02d}.npy'.format(i), samples)\n",
+    "    subposteriors.append(samples)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### merge subposteriors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "consensus_samples = consensus(subposteriors, 10000)\n",
+    "parametric_samples = parametric_draws(subposteriors, 10000)\n",
+    "np.save('.results/consensus_samples.npy', consensus_samples)\n",
+    "np.save('.results/parametric_samples.npy', parametric_samples)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### predict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def predict(model, X, rng, sample):\n",
+    "    model = substitute(seed(model, rng), sample)\n",
+    "    model_trace = trace(model).get_trace(X, None)\n",
+    "    return model_trace['y']['value']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Consensus accuaracy: 0.771\n",
+      "Parametric accuaracy: 0.771\n"
+     ]
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(2), 10000)\n",
+    "\n",
+    "y_consensus = vmap(partial(predict, model, X_test))(rngs, consensus_samples)\n",
+    "y_consensus = (y_consensus.sum(axis=0) / y_consensus.shape[0]) >= 0.5\n",
+    "acc = (y_consensus == y_test).sum() / y_test.shape[0]\n",
+    "print('Consensus accuaracy: {}'.format(round(acc.item(), 4)))\n",
+    "\n",
+    "y_parametric = vmap(partial(predict, model, X_test))(rngs, parametric_samples)\n",
+    "y_parametric = (y_parametric.sum(axis=0) / y_parametric.shape[0]) >= 0.5\n",
+    "acc = (y_parametric == y_test).sum() / y_test.shape[0]\n",
+    "print('Parametric accuaracy: {}'.format(round(acc.item(), 4)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### train iaf"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rng_guide, rng_init, rng_train = random.split(random.PRNGKey(3), 3)\n",
+    "opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
+    "guide = AutoIAFNormal(rng_guide, model, get_params, nonlinearity=stax.Elu,\n",
+    "                      skip_connections=False)\n",
+    "batch_size = 1000\n",
+    "ll_scale = X_train.shape[0] // batch_size\n",
+    "svi_init, svi_update, _ = svi(model, guide, elbo, opt_init, opt_update, get_params,\n",
+    "                              likelihood_scale=ll_scale)\n",
+    "num_iters = ll_scale\n",
+    "\n",
+    "def epoch_train(epoch, opt_state, rng):\n",
+    "    # shuffle data\n",
+    "    rng, rng_shuffle = random.split(rng)\n",
+    "    idx = random.shuffle(rng_shuffle, np.arange(X_train.shape[0]))\n",
+    "    X = X_train[idx]\n",
+    "    y = y_train[idx]\n",
+    "    offset = epoch * num_iters\n",
+    "\n",
+    "    def body_fn(val, i):\n",
+    "        batch_X = lax.dynamic_slice_in_dim(X, i * batch_size, batch_size)\n",
+    "        batch_y = lax.dynamic_slice_in_dim(y, i * batch_size, batch_size)\n",
+    "        opt_state_, rng_ = val\n",
+    "        loss, opt_state_, rng_ = svi_update(offset + i, rng_, opt_state_,\n",
+    "                                            (batch_X, batch_y), (batch_X, batch_y))\n",
+    "        return (opt_state_, rng_), loss\n",
+    "\n",
+    "    (opt_state, _), losses = lax.scan(body_fn, (opt_state, rng), np.arange(num_iters))\n",
+    "    return opt_state, losses"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "opt_state, _ = svi_init(rng_init,\n",
+    "                        (X_train[:batch_size], y_train[:batch_size]),\n",
+    "                        (X_train[:batch_size], y_train[:batch_size]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 00 - loss 1883.5496 - acc 0.7612\n",
+      "Epoch 01 - loss 688.8702 - acc 0.7706\n",
+      "Epoch 02 - loss 617.3635 - acc 0.7685\n",
+      "Epoch 03 - loss 601.3757 - acc 0.7711\n",
+      "Epoch 04 - loss 598.3813 - acc 0.7687\n",
+      "Epoch 05 - loss 593.7759 - acc 0.7708\n",
+      "Epoch 06 - loss 593.0955 - acc 0.7692\n",
+      "Epoch 07 - loss 590.5724 - acc 0.7714\n",
+      "Epoch 08 - loss 589.2113 - acc 0.7693\n",
+      "Epoch 09 - loss 588.8226 - acc 0.7721\n"
+     ]
+    }
+   ],
+   "source": [
+    "losses = np.array([])\n",
+    "num_epochs = 10\n",
+    "rngs = random.split(random.PRNGKey(2), 10000)\n",
+    "for epoch in range(num_epochs):\n",
+    "    rng = random.fold_in(rng_train, epoch)\n",
+    "    opt_state, epoch_loss = epoch_train(epoch, opt_state, rng)\n",
+    "    iaf_samples = guide.sample_posterior(random.PRNGKey(4), opt_state, sample_shape=(10000,))\n",
+    "    y_iaf = vmap(partial(predict, model, X_test))(rngs, iaf_samples)\n",
+    "    y_iaf = (y_iaf.sum(axis=0) / y_iaf.shape[0]) >= 0.5\n",
+    "    acc = (y_iaf == y_test).sum() / y_test.shape[0]\n",
+    "    print(\"Epoch {:02d} - loss {:.4f} - acc {}\".format(\n",
+    "        epoch, np.mean(epoch_loss), round(acc.item(), 4)))\n",
+    "    losses = np.concatenate([losses, epoch_loss])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Flow HMC"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "transform = guide.get_transform(opt_state)\n",
+    "unpack_fn = guide.unpack_latent\n",
+    "latent_size = guide.latent_size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def make_transformed_pe(potential_fn, transform, unpack_fn, prior_scale):\n",
+    "    def transformed_potential_fn(z):\n",
+    "        u, intermediates = transform.call_with_intermediates(z)\n",
+    "        logdet = transform.log_abs_det_jacobian(z, u, intermediates=intermediates) * prior_scale\n",
+    "        return potential_fn(unpack_fn(u)) + logdet\n",
+    "\n",
+    "    return transformed_potential_fn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_flow_subposterior(rng, shard, K):\n",
+    "    X, y = shard\n",
+    "    init_params = random.normal(rng, (4, latent_size))\n",
+    "    _, potential_fn, _ = initialize_model(rng, model, X, y, prior_scale=1 / K)\n",
+    "    transformed_potential_fn = make_transformed_pe(potential_fn, transform, unpack_fn, 1 / K)\n",
+    "    samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
+    "                   num_chains=4, potential_fn=transformed_potential_fn)\n",
+    "    return samples"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "warmup: 100%|██████████| 1000/1000 [03:07<00:00,  5.63it/s, 1023 steps of size 6.92e-05. acc. prob=0.78]\n",
+      "sample: 100%|██████████| 2500/2500 [07:29<00:00,  5.58it/s, 1023 steps of size 6.92e-05. acc. prob=0.88]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "\n",
+      "                 mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      " Param:0[0]    -13.94      0.25    -14.01    -14.26    -13.50      6.02      1.01\n",
+      " Param:0[1]      3.60      0.10      3.58      3.46      3.77      4.80      1.81\n",
+      " Param:0[2]     -1.00      0.36     -1.06     -1.56     -0.42      4.99      1.35\n",
+      " Param:0[3]     -5.20      0.33     -5.32     -5.57     -4.54      3.37      1.68\n",
+      " Param:0[4]     -2.45      0.67     -2.45     -3.60     -1.51      2.59      2.69\n",
+      " Param:0[5]      6.63      0.44      6.74      5.81      7.18      3.79      1.65\n",
+      " Param:0[6]      0.34      0.57      0.30     -0.56      1.29      7.26      1.01\n",
+      " Param:0[7]     -1.72      0.30     -1.72     -2.22     -1.24      4.35      1.86\n",
+      " Param:0[8]     10.02      0.59      9.89      9.13     11.04      4.90      1.15\n",
+      " Param:0[9]     -6.03      0.49     -5.89     -6.84     -5.33      3.51      1.69\n",
+      "Param:0[10]     11.40      0.53     11.44     10.59     12.21      3.57      2.19\n",
+      "Param:0[11]     15.31      0.38     15.24     14.73     15.97     12.57      1.01\n",
+      "Param:0[12]     30.34      0.88     30.54     28.70     31.54      5.96      1.01\n",
+      "Param:0[13]     -0.24      0.57     -0.25     -1.15      0.54      4.01      1.41\n",
+      "Param:0[14]     -8.89      0.47     -8.82     -9.67     -8.16      4.70      1.05\n",
+      "Param:0[15]      0.82      0.64      0.97     -0.55      1.62      4.95      1.11\n",
+      "Param:0[16]      0.62      0.32      0.54      0.20      1.18      4.59      1.12\n",
+      "Param:0[17]    -10.90      1.00    -10.76    -12.52     -9.27      5.20      1.45\n",
+      "Param:0[18]      0.62      0.16      0.59      0.37      0.86      4.88      1.16\n",
+      "Param:0[19]     -6.58      0.50     -6.55     -7.44     -5.74      8.45      1.00\n",
+      "Param:0[20]    -14.14      0.68    -14.13    -15.11    -13.16      2.59      2.48\n",
+      "Param:0[21]      5.05      0.25      4.98      4.72      5.46      3.38      1.72\n",
+      "Param:0[22]      1.46      0.41      1.49      0.84      2.22      3.58      1.89\n",
+      "Param:0[23]     -4.04      0.42     -4.07     -4.73     -3.47      3.97      1.82\n",
+      "Param:0[24]     -7.94      1.89     -7.75    -11.41     -5.26      2.97      2.36\n",
+      "Param:0[25]     -0.50      0.55     -0.55     -1.22      0.30      2.99      2.22\n",
+      "Param:0[26]     -2.05      0.53     -2.09     -2.85     -1.06      9.19      1.39\n",
+      "Param:0[27]      5.06      1.25      5.22      3.21      7.47      4.65      1.36\n",
+      "Param:0[28]      8.44      0.82      8.39      7.00      9.66      4.58      1.64\n",
+      "Param:0[29]      0.19      0.28      0.26     -0.38      0.54      3.76      1.61\n",
+      "Param:0[30]     14.60      1.78     15.01     11.66     17.62      3.66      1.63\n",
+      "Param:0[31]     20.82      0.90     20.76     19.62     22.35      5.42      1.29\n",
+      "Param:0[32]    -31.48      3.68    -31.31    -37.17    -25.47      5.27      1.00\n",
+      "Param:0[33]    -42.52      1.82    -42.42    -45.33    -39.70     26.26      1.01\n",
+      "Param:0[34]    -49.77      3.01    -50.29    -54.42    -46.00      2.74      2.70\n",
+      "Param:0[35]     17.45      2.33     17.69     13.41     21.19      4.13      1.76\n",
+      "Param:0[36]      4.63      6.34      5.31     -5.43     13.28      3.42      1.61\n",
+      "Param:0[37]     13.86      4.16     12.31      8.42     20.54      4.86      1.02\n",
+      "Param:0[38]      0.78      1.44      0.71     -1.81      2.61     13.06      1.09\n",
+      "Param:0[39]     28.69      2.32     27.99     25.57     32.94      4.43      1.47\n",
+      "Param:0[40]    -20.61      2.50    -20.76    -23.80    -16.05      7.42      1.47\n",
+      "Param:0[41]    -53.15      9.93    -51.85    -68.62    -35.56      7.21      1.08\n",
+      "Param:0[42]      2.50      2.45      2.10     -1.07      5.54     10.09      1.02\n",
+      "Param:0[43]      0.90      0.26      0.88      0.53      1.41      3.39      2.19\n",
+      "Param:0[44]    -99.67      4.76    -98.73   -107.37    -92.83      6.72      1.09\n",
+      "Param:0[45]   -115.56     11.62   -116.65   -134.54    -93.48      8.19      1.00\n",
+      "Param:0[46]     -1.78      0.41     -1.73     -2.51     -1.21      4.37      1.60\n",
+      "Param:0[47]    106.94      5.34    107.00     98.59    115.20      6.45      1.00\n",
+      "Param:0[48]      9.21      1.05      9.52      7.30     10.58      3.92      1.52\n",
+      "Param:0[49]     23.49     11.20     26.47      1.60     37.24      3.97      1.60\n",
+      "Param:0[50]     -3.87      0.64     -3.84     -5.00     -2.86     11.39      1.01\n",
+      "Param:0[51]    -30.30      4.26    -29.63    -39.68    -24.57      5.93      1.08\n",
+      "Param:0[52]      9.28      0.64      9.41      7.95     10.14      6.93      1.01\n",
+      "Param:0[53]     22.34      4.76     20.76     16.82     31.59      3.29      1.54\n",
+      "Param:0[54]    262.73     36.32    270.82    191.77    306.70      8.09      1.05\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "init_params = random.normal(random.PRNGKey(1), (latent_size,))\n",
+    "_, potential_fn, _ = initialize_model(rng, model, X, y, prior_scale=1 / K)\n",
+    "transformed_potential_fn = make_transformed_pe(potential_fn, transform, unpack_fn, 1 / K)\n",
+    "samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n",
+    "               num_chains=1, potential_fn=transformed_potential_fn)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "flow_samples = vmap(lambda x: unpack_fn(transform(x)))(samples)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from numpyro.diagnostics import summary"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "DeviceArray(0.7682474, dtype=float32)"
+      ]
+     },
+     "execution_count": 97,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(2), 2500)\n",
+    "y_flow = vmap(partial(predict, model, X_test))(rngs, flow_samples)\n",
+    "y_flow = (y_flow.sum(axis=0) / y_flow.shape[0]) >= 0.5\n",
+    "acc = (y_flow == y_test).sum() / y_test.shape[0]\n",
+    "acc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "\n",
+      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
+      "  coefs[0]      1.97      0.07      1.97      1.86      2.09     17.99      1.01\n",
+      "  coefs[1]     -0.02      0.02     -0.02     -0.05      0.02     21.80      1.02\n",
+      "  coefs[2]     -0.12      0.02     -0.12     -0.14     -0.08      8.34      1.05\n",
+      "  coefs[3]     -0.31      0.02     -0.31     -0.34     -0.28      7.72      1.17\n",
+      "  coefs[4]     -0.11      0.02     -0.11     -0.14     -0.08     10.66      1.01\n",
+      "  coefs[5]     -0.10      0.02     -0.09     -0.12     -0.07     65.96      1.00\n",
+      "  coefs[6]      0.01      0.02      0.01     -0.03      0.05      7.04      1.15\n",
+      "  coefs[7]     -0.49      0.03     -0.49     -0.53     -0.44     14.74      1.00\n",
+      "  coefs[8]      0.24      0.02      0.23      0.20      0.27      5.82      1.47\n",
+      "  coefs[9]     -0.01      0.01     -0.01     -0.03      0.02      6.66      1.48\n",
+      " coefs[10]      1.67      0.04      1.68      1.61      1.74      6.33      1.03\n",
+      " coefs[11]      0.53      0.02      0.53      0.49      0.57     11.40      1.22\n",
+      " coefs[12]      1.44      0.03      1.44      1.39      1.50      7.69      1.05\n",
+      " coefs[13]     -0.80      0.22     -0.81     -1.13     -0.50      3.51      1.65\n",
+      " coefs[14]     -2.65      0.16     -2.65     -2.92     -2.38     10.49      1.06\n",
+      " coefs[15]     -0.95      0.16     -0.92     -1.23     -0.68      5.82      1.14\n",
+      " coefs[16]     -0.74      0.12     -0.78     -0.90     -0.53      4.76      1.15\n",
+      " coefs[17]     -0.21      0.02     -0.20     -0.25     -0.17     17.49      1.02\n",
+      " coefs[18]     -0.06      0.11     -0.07     -0.23      0.12      5.46      1.10\n",
+      " coefs[19]     -1.63      0.07     -1.63     -1.73     -1.50      8.42      1.22\n",
+      " coefs[20]     -2.43      0.15     -2.45     -2.66     -2.20      2.83      2.25\n",
+      " coefs[21]      0.00      0.02     -0.00     -0.03      0.03      6.51      1.23\n",
+      " coefs[22]     -0.03      0.02     -0.03     -0.07      0.00      3.49      2.16\n",
+      " coefs[23]     -0.14      0.04     -0.14     -0.22     -0.09      3.17      2.54\n",
+      " coefs[24]     -0.17      0.04     -0.17     -0.25     -0.11      4.80      1.64\n",
+      " coefs[25]     -0.02      0.03     -0.02     -0.05      0.03      4.50      1.61\n",
+      " coefs[26]     -0.04      0.01     -0.04     -0.06     -0.02     10.97      1.32\n",
+      " coefs[27]     -1.01      0.05     -1.00     -1.10     -0.94      6.59      1.02\n",
+      " coefs[28]      0.36      0.36      0.35     -0.23      0.93      2.95      2.12\n",
+      " coefs[29]      0.09      0.02      0.09      0.06      0.12      5.30      1.13\n",
+      " coefs[30]      0.10      0.03      0.10      0.05      0.15     32.94      1.14\n",
+      " coefs[31]      0.05      0.04      0.05     -0.02      0.11      9.05      1.01\n",
+      " coefs[32]      0.12      0.01      0.12      0.10      0.13      4.93      1.31\n",
+      " coefs[33]      0.11      0.01      0.11      0.09      0.14      9.51      1.19\n",
+      " coefs[34]      0.07      0.03      0.07      0.02      0.12     40.27      1.01\n",
+      " coefs[35]      0.35      0.02      0.35      0.32      0.38      4.23      1.46\n",
+      " coefs[36]      0.36      0.02      0.36      0.33      0.38     10.62      1.04\n",
+      " coefs[37]      0.16      0.01      0.16      0.14      0.18     11.52      1.00\n",
+      " coefs[38]     -0.02      0.02     -0.02     -0.05      0.01     27.97      1.04\n",
+      " coefs[39]     -0.01      0.03     -0.01     -0.05      0.03     17.64      1.04\n",
+      " coefs[40]      0.00      0.02      0.00     -0.04      0.04     16.42      1.15\n",
+      " coefs[41]     -1.13      0.11     -1.12     -1.31     -0.99      8.21      1.09\n",
+      " coefs[42]      0.09      0.02      0.09      0.07      0.12      9.71      1.28\n",
+      " coefs[43]     -0.08      0.02     -0.07     -0.12     -0.04      8.79      1.26\n",
+      " coefs[44]      0.14      0.02      0.15      0.10      0.18      5.45      1.52\n",
+      " coefs[45]      0.09      0.02      0.08      0.06      0.12     15.35      1.09\n",
+      " coefs[46]      0.16      0.02      0.16      0.14      0.19     20.08      1.02\n",
+      " coefs[47]     -0.01      0.03     -0.01     -0.06      0.05     22.08      1.16\n",
+      " coefs[48]     -0.09      0.02     -0.09     -0.11     -0.05     27.91      1.19\n",
+      " coefs[49]      1.08      0.15      1.07      0.83      1.31      6.21      1.15\n",
+      " coefs[50]     -1.99      0.29     -1.95     -2.48     -1.56     15.78      1.00\n",
+      " coefs[51]     -0.11      0.02     -0.11     -0.14     -0.07     11.80      1.24\n",
+      " coefs[52]     -0.13      0.02     -0.12     -0.16     -0.10     18.72      1.00\n",
+      " coefs[53]     -0.15      0.02     -0.15     -0.19     -0.12     48.88      1.03\n",
+      " coefs[54]     -2.20      0.06     -2.21     -2.28     -2.09      4.78      1.54\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "summary({'coefs': real_samples['coefs'][None, ...]})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X, y = shards[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      " =============================== SUBPOSTERIOR 00 ===============================\n",
+      "\n",
+      "                 mean       std    median      5.0%     95.0%     n_eff     r_hat\n"
+     ]
+    },
+    {
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-51-124cdeca60c4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0msep\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'='\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m31\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'\\n '\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msep\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m' SUBPOSTERIOR {:02d} '\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0msamples\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_flow_subposterior\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrng\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshard\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'.results/flow'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmakedirs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'.results/flow'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-50-01ecbd4c636c>\u001b[0m in \u001b[0;36mget_flow_subposterior\u001b[0;34m(rng, shard, K)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mtransformed_potential_fn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_transformed_pe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpotential_fn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransform\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0munpack_fn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     samples = mcmc(num_warmup=1000, num_samples=2500, init_params=init_params,\n\u001b[0;32m----> 7\u001b[0;31m                    num_chains=4, potential_fn=transformed_potential_fn)\n\u001b[0m\u001b[1;32m      8\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0msamples\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/numpyro/numpyro/mcmc.py\u001b[0m in \u001b[0;36mmcmc\u001b[0;34m(num_warmup, num_samples, init_params, num_chains, sampler, constrain_fn, print_summary, **sampler_kwargs)\u001b[0m\n\u001b[1;32m    425\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    426\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mprint_summary\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 427\u001b[0;31m             \u001b[0msummary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msamples\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    428\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0msamples_flat\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    429\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/numpyro/numpyro/diagnostics.py\u001b[0m in \u001b[0;36msummary\u001b[0;34m(samples, prob)\u001b[0m\n\u001b[1;32m    223\u001b[0m     \u001b[0mrow_format\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname_format\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m' {:>9.2f} {:>9.2f} {:>9.2f} {:>9.2f} {:>9.2f} {:>9.2f} {:>9.2f}'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    224\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msamples\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 225\u001b[0;31m         \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdevice_get\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    226\u001b[0m         \u001b[0mvalue_flat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0monp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    227\u001b[0m         \u001b[0mmean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue_flat\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/miniconda3/envs/pydata/lib/python3.6/site-packages/jax/api.py\u001b[0m in \u001b[0;36mdevice_get\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m   1109\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0my\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtree_leaves\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1110\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1111\u001b[0;31m       \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy_to_host_async\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1112\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1113\u001b[0m       \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/miniconda3/envs/pydata/lib/python3.6/site-packages/jax/interpreters/pxla.py\u001b[0m in \u001b[0;36mcopy_to_host_async\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    448\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_npy_value\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    449\u001b[0m       \u001b[0;32mfor\u001b[0m \u001b[0mbuf\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdevice_buffers\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 450\u001b[0;31m         \u001b[0mbuf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy_to_host_async\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    451\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    452\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mdelete\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+     ]
+    }
+   ],
+   "source": [
+    "rngs = random.split(random.PRNGKey(1), K)\n",
+    "subposteriors = []\n",
+    "for i, (rng, shard) in enumerate(zip(rngs, shards)):\n",
+    "    if i > 0:\n",
+    "        break\n",
+    "    sep = '=' * 31\n",
+    "    print('\\n ' + sep + ' SUBPOSTERIOR {:02d} '.format(i) + sep, end='')\n",
+    "    samples = get_flow_subposterior(rng, shard, K)\n",
+    "    if not os.path.exists('.results/flow'):\n",
+    "        os.makedirs('.results/flow')\n",
+    "    np.save('.results/flow/subposterior_{:02d}.npy'.format(i), samples)\n",
+    "    subposteriors.append(samples)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python (pydata)",
+   "language": "python",
+   "name": "pydata"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

From 7e3064bcf82fc25941052efe071a40a2da8c32bd Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Tue, 17 Sep 2019 16:46:01 -0400
Subject: [PATCH 24/35] add block neural arn implementation

---
 numpyro/contrib/nn/block_neural_arn.py | 130 +++++++++++++++++++++++++
 numpyro/contrib/nn/bna_nn.py           |  53 ----------
 numpyro/contrib/nn/masked_dense.py     |   2 +
 numpyro/distributions/constraints.py   |   3 +-
 numpyro/distributions/util.py          |  13 +++
 5 files changed, 147 insertions(+), 54 deletions(-)
 create mode 100644 numpyro/contrib/nn/block_neural_arn.py
 delete mode 100644 numpyro/contrib/nn/bna_nn.py

diff --git a/numpyro/contrib/nn/block_neural_arn.py b/numpyro/contrib/nn/block_neural_arn.py
new file mode 100644
index 000000000..c43d88d02
--- /dev/null
+++ b/numpyro/contrib/nn/block_neural_arn.py
@@ -0,0 +1,130 @@
+from jax import ops, random
+from jax.nn.initializer import glorot_uniform, normal, uniform
+
+from numpyro.distributions.util import softplus
+
+
+def BlockMaskedDense(num_blocks, in_factor, out_factor, bias=True, W_init=glorot_uniform()):
+    """
+    Module that implements a linear layer with block matrices with positive diagonal blocks.
+    Moreover, it uses Weight Normalization (https://arxiv.org/abs/1602.07868) for stability.
+
+    :param int num_blocks: Number of block matrices.
+    :param int in_factor: number of rows in each block.
+    :param int out_factor: number of columns in each block.
+    :param W_init: initialization method for the weights.
+    :return: an (`init_fn`, `update_fn`) pair.
+    """
+    input_dim, out_dim = num_blocks * in_factor, num_blocks * out_factor
+    # construct mask_d, mask_o for formula (8) of Ref [1]
+    # Diagonal block mask
+    mask_d = np.identity(num_block)[..., None]
+    mask_d = np.tile(mask_d, (1, in_factor, out_factor)).reshape(input_dim, out_dim)
+    # Off-diagonal block mask for lower triangular weight matrix
+    mask_o = vec_to_tril_matrix(np.ones(dim * (dim - 1) // 2), diagonal=-1)[..., None]
+    mask_o = np.tile(mask_o, (1, in_factor, out_factor)).reshape(input_dim, out_dim)
+
+    def init_fun(rng, input_shape):
+        assert input_dim == input_shape[-1]
+        *k1, k2, k3 = random.split(rng, num_blocks + 2)
+
+        # Initialize each column block using W_init
+        W = np.zeros((input_dim, out_dim)
+        for i in range(num_blocks):
+            W = ops.index_add(
+                W,
+                ops.index[:(i + 1) * in_factor, i * out_factor:(i + 1) * out_factor],
+                W_init(k1[i], ((i + 1) * in_factor, out_factor))
+            )
+
+        # initialize weight scale
+        ws = np.log(uniform(1.)(k2, (out_dim,)))
+
+        if bias:
+            b = (uniform(1.)(k3, mask.shape[-1:]) - 0.5) * (2 / np.sqrt(out_dim))
+            params = (W, ws, b)
+        else:
+            params = (W, ws)
+        return input_shape[:-1] + (outdim,), params
+
+    def apply_fun(params, inputs, **kwargs):
+        x, logdet = inputs
+        if bias:
+            W, ws, b = params
+        else:
+            W, ws = params
+
+        # Form block weight matrix, making sure it's positive on diagonal!
+        w = np.exp(W) * mask_d + W * mask_o
+
+        # Compute norm of each column (i.e. each output features)
+        w_norm = np.linalg.norm(w ** 2, axis=-2, keepdims=True)
+
+        # Normalize weight and rescale
+        w = np.exp(ws) * w / w_norm
+
+        out = np.dot(x, w)
+        if bias:
+            out = out + b
+
+        dense_logdet = ws + W - np.log(w_norm)
+        # logdet of block diagonal
+        dense_logdet = logdet[mask_d.astype(bool)].reshape(dim, in_factor, out_factor)
+        logdet = dense_logdet if logdet is None else logmatmulexp(logdet, dense_logdet)
+        return out, logdet
+
+    return init_fun, apply_fun
+
+
+def Tanh():
+    def init_fun(rng, input_shape):
+        return input_shape, ()
+
+    def apply_fun(params, inputs, **kwargs):
+        x, logdet = inputs
+        out = np.tanh(x)
+        tanh_logdet = -2 * (s + softplus(-2 * s)- np.log(2.))
+        # logdet.shape = batch_shape + (num_blocks, in_factor, out_factor)
+        # tanh_logdet.shape = batch_shape + (num_blocks x out_factor,)
+        # so we need to reshape tanh_logdet to: batch_shape + (num_blocks, 1, out_factor)
+        tanh_logdet = tanh_logdet.reshape(logdet.shape[:-2] + (1, logdet.shape[-1]))
+        return out, logdet + tanh_logdet
+
+
+def FanInNormal():
+    """
+    Similar to stax.FanInSum but also keeps track of log determinant of Jacobian.
+    """
+    # x + f(x)
+    def init_fun(rng, input_shape):
+        pass
+
+    def apply_fun(params, inputs, **kwargs):
+        pass
+
+
+def FanInGated(gate_init=normal(1.)):
+    """
+    Similar to FanInNormal uses a learnable parameter `gate` to interpolate two fan-in branches.
+    """
+    # a * x + (1 - a) * f(x)
+    def init_fun(rng, input_shape):
+        pass
+
+    def apply_fun(params, inputs, **kwargs):
+        pass
+
+
+def BlockNeuralAutoregressiveNN(input_dim, hidden_factors, residual=None):
+    layers = []
+    in_factor = 1
+    for i, hidden_factor in enumerate(hidden_factors):
+        layers.append(BlockMaskedDense(input_dim, in_factor, hidden_factor))
+        layers.append(Tanh())
+        in_factor = hidden_factor
+    layers.append(BlockMaskedDense(input_dim, in_factor, 1))
+    arn = stax.serial(*layers)
+    if residual is None
+        return arn
+    else:
+        return stax.serial(stax.FanOut(2), stax.parallel(stax.Identity, arn), residual())
diff --git a/numpyro/contrib/nn/bna_nn.py b/numpyro/contrib/nn/bna_nn.py
deleted file mode 100644
index 81e9650a8..000000000
--- a/numpyro/contrib/nn/bna_nn.py
+++ /dev/null
@@ -1,53 +0,0 @@
-from numpyro.distributions.util import softplus
-
-
-def MaskedBlockDense():
-    def init_fun(rng, input_shape):
-        return output_shape, params
-
-    def apply_fun(params, inputs, **kwargs):
-        x, logdet = inputs
-        # TODO: implement
-        return o, logdet
-
-
-def Tanh():
-    def init_fun(rng, input_shape):
-        return input_shape, ()
-
-    def apply_fun(params, inputs, **kwargs):
-        x, logdet = inputs
-        y = np.tanh(x)
-        tanh_logdet = - 2 * (x - np.log(2.) + softplus(-2 * x))
-        return y, logdet + tanh_logdet  # TODO: reshape?
-
-
-def stax_serial_with_jacobian(*layers):
-    """
-    Works like `stax.serial` but also forward the log determinant of Jacobian.
-    """
-    nlayers = len(layers)
-    init_funs, apply_funs = zip(*layers)
-
-    def init_fun(rng, input_shape):
-        params = []
-        for init_fun in init_funs:
-          rng, layer_rng = random.split(rng)
-          input_shape, param = init_fun(layer_rng, input_shape)
-          params.append(param)
-        return input_shape, params
-
-    def apply_fun(params, inputs, **kwargs):
-        rng = kwargs.pop('rng', None)
-        rngs = random.split(rng, nlayers) if rng is not None else (None,) * nlayers
-        for fun, param, rng in zip(apply_funs, params, rngs):
-          inputs = fun(param, inputs, rng=rng, **kwargs)
-        return inputs
-
-    return init_fun, apply_fun
-
-
-def BlockNeuralAutoregressiveNN(input_dim, hidden_factor):
-    # TODO: support multi hidden factors
-    layers = [MaskedBlockDense(hidden_factor), Tanh(), MaskedBlockDense(input_dim)]
-    return stax_serial_with_jacobian(*layers)
diff --git a/numpyro/contrib/nn/masked_dense.py b/numpyro/contrib/nn/masked_dense.py
index a1593c319..ce0459787 100644
--- a/numpyro/contrib/nn/masked_dense.py
+++ b/numpyro/contrib/nn/masked_dense.py
@@ -2,6 +2,8 @@
 from jax.experimental.stax import glorot, randn
 import jax.numpy as np
 
+from numpyro.distributions.util import vec_to_tril_matrix
+
 
 def MaskedDense(mask, bias=True, W_init=glorot(), b_init=randn()):
     """
diff --git a/numpyro/distributions/constraints.py b/numpyro/distributions/constraints.py
index 190944835..51379088c 100644
--- a/numpyro/distributions/constraints.py
+++ b/numpyro/distributions/constraints.py
@@ -35,6 +35,7 @@
     get_dtype,
     matrix_to_tril_vec,
     signed_stick_breaking_tril,
+    softplus,
     sum_rightmost,
     vec_to_tril_matrix
 )
@@ -361,7 +362,7 @@ def log_abs_det_jacobian(self, x, y, intermediates=None):
         z1m_cumprod_tril = matrix_to_tril_vec(z1m_cumprod, diagonal=-2)
         stick_breaking_logdet = 0.5 * np.sum(np.log(z1m_cumprod_tril), axis=-1)
 
-        tanh_logdet = -2 * np.sum(np.log(np.cosh(x)), axis=-1)
+        tanh_logdet = -2 * np.sum(x + softplus(-2 * x) - np.log(2.), axis=-1)
         return stick_breaking_logdet + tanh_logdet
 
 
diff --git a/numpyro/distributions/util.py b/numpyro/distributions/util.py
index 168863d6b..1c19051dd 100644
--- a/numpyro/distributions/util.py
+++ b/numpyro/distributions/util.py
@@ -171,12 +171,14 @@ def cholesky_inverse(matrix):
     return solve_triangular(tril_inv, identity, lower=True)
 
 
+# TODO: move upstream to jax.nn
 def binary_cross_entropy_with_logits(x, y):
     # compute -y * log(sigmoid(x)) - (1 - y) * log(1 - sigmoid(x))
     # Ref: https://www.tensorflow.org/api_docs/python/tf/nn/sigmoid_cross_entropy_with_logits
     return np.clip(x, 0) + np.log1p(np.exp(-np.abs(x))) - x * y
 
 
+# TODO: use upstream jax.nn.softmax
 def softmax(x, axis=-1):
     unnormalized = np.exp(x - np.max(x, axis, keepdims=True))
     return unnormalized / np.sum(unnormalized, axis, keepdims=True)
@@ -263,10 +265,21 @@ def signed_stick_breaking_tril(t):
     return y
 
 
+# TODO: use upstream jax.nn.softplus
 def softplus(x):
     return np.logaddexp(x, 0.)
 
 
+def logmatmulexp(x, y):
+    """
+    Numerically stable version of ``(x.log() @ y.log()).exp()``.
+    """
+    x_shift = np.amax(x, -1, keepdims=True)
+    y_shift = np.amax(y, -2, keepdims=True)
+    xy = np.log(np.matmul((x - x_shift).exp(), (y - y_shift).exp()))
+    return xy + x_shift + y_shift
+
+
 # The is sourced from: torch.distributions.util.py
 #
 # Copyright (c) 2016-     Facebook, Inc            (Adam Paszke)

From 0e95a9b0c37abd411bdd2eb1dd4c86b924185a7f Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Tue, 17 Sep 2019 22:50:24 -0400
Subject: [PATCH 25/35] implement residual gate

---
 numpyro/contrib/nn/block_neural_arn.py | 60 +++++++++++++++++++++-----
 numpyro/distributions/flows.py         | 42 ++++++++++--------
 2 files changed, 74 insertions(+), 28 deletions(-)

diff --git a/numpyro/contrib/nn/block_neural_arn.py b/numpyro/contrib/nn/block_neural_arn.py
index c43d88d02..cd39153be 100644
--- a/numpyro/contrib/nn/block_neural_arn.py
+++ b/numpyro/contrib/nn/block_neural_arn.py
@@ -1,7 +1,8 @@
 from jax import ops, random
+from jax.experimental import stax
+from jax.nn import softplus
 from jax.nn.initializer import glorot_uniform, normal, uniform
-
-from numpyro.distributions.util import softplus
+import jax.numpy as np
 
 
 def BlockMaskedDense(num_blocks, in_factor, out_factor, bias=True, W_init=glorot_uniform()):
@@ -77,6 +78,11 @@ def apply_fun(params, inputs, **kwargs):
 
 
 def Tanh():
+    """
+    Tanh nonlinearity with its log jacobian.
+
+    :return: an (`init_fn`, `update_fn`) pair.
+    """
     def init_fun(rng, input_shape):
         return input_shape, ()
 
@@ -90,32 +96,64 @@ def apply_fun(params, inputs, **kwargs):
         tanh_logdet = tanh_logdet.reshape(logdet.shape[:-2] + (1, logdet.shape[-1]))
         return out, logdet + tanh_logdet
 
+    return init_fun, apply_fun
 
-def FanInNormal():
+
+def FanInResidualNormal():
     """
     Similar to stax.FanInSum but also keeps track of log determinant of Jacobian.
+    It is required that the second fan-in branch is identity.
+
+    :return: an (`init_fn`, `update_fn`) pair.
     """
-    # x + f(x)
     def init_fun(rng, input_shape):
-        pass
+        return input_shape[0], ()
 
     def apply_fun(params, inputs, **kwargs):
-        pass
+        # f(x) + x
+        (fx, logdet), (x, _) = inputs
+        return fx + x, softplus(logdet)
+
+    return init_fun, apply_fun
 
 
-def FanInGated(gate_init=normal(1.)):
+def FanInResidualGated(gate_init=normal(1.)):
     """
     Similar to FanInNormal uses a learnable parameter `gate` to interpolate two fan-in branches.
+    It is required that the second fan-in branch is identity.
+
+    :param gate_init: initialization method for the gate.
+    :return: an (`init_fn`, `update_fn`) pair.
     """
-    # a * x + (1 - a) * f(x)
     def init_fun(rng, input_shape):
-        pass
+        return input_shape[0], gate_init(rng, ())
 
     def apply_fun(params, inputs, **kwargs):
-        pass
+        # a * f(x) + (1 - a) * x
+        (fx, logdet), (x, _) = inputs
+        gate = np.sigmoid(params)
+        out = gate * fx + (1 - gate) * x
+        logdet = softplus(logdet + params) - softplus(params)
+        return out, logdet
+
+    return init_fun, apply_fun
 
 
 def BlockNeuralAutoregressiveNN(input_dim, hidden_factors, residual=None):
+    """
+    An implementation of Block Neural Autoregressive neural network.
+
+    **References**
+
+    1. *Block Neural Autoregressive Flow*,
+       Nicola De Cao, Ivan Titov, Wilker Aziz
+
+    :param int input_dim: The dimensionality of the input.
+    :param list hidden_factors: Hidden layer i has ``hidden_factors[i]`` hidden units per
+        input dimension. This corresponds to both :math:`a` and :math:`b` in reference [1].
+        The elements of hidden_factors must be integers.
+    :param residual: Type of residual connections to use.
+    """
     layers = []
     in_factor = 1
     for i, hidden_factor in enumerate(hidden_factors):
@@ -127,4 +165,4 @@ def BlockNeuralAutoregressiveNN(input_dim, hidden_factors, residual=None):
     if residual is None
         return arn
     else:
-        return stax.serial(stax.FanOut(2), stax.parallel(stax.Identity, arn), residual())
+        return stax.serial(stax.FanOut(2), stax.parallel(arn, stax.Identity), residual())
diff --git a/numpyro/distributions/flows.py b/numpyro/distributions/flows.py
index f3e922908..ef65e3aa3 100644
--- a/numpyro/distributions/flows.py
+++ b/numpyro/distributions/flows.py
@@ -83,25 +83,33 @@ def log_abs_det_jacobian(self, x, y, intermediates=None):
 class BlockNeuralAutoregressiveTransform(Transform):
     event_dim = 1
 
-    def __init__(self, bna_nn, params):
-        self.bna_nn = bna_nn
-        self.params = params
+    def __init__(self, bn_arn):
+        self.bn_arn = bn_arn
 
     def __call__(self, x):
-        self._cached_x = x
-        y, self._cached_logdet = self.bna_nn(self.params, x)
-        return y
+        """
+        :param numpy.ndarray x: the input into the transform
+        """
+        return self.call_with_intermediates(x)[0]
 
-    def inv(self, y, caching=True):
-        if caching:
-            return self._cached_x
-        else:
-            raise ValueError("Block neural autoregressive transform does not have an analytic"
-                             " inverse implemented.")
+    def call_with_intermediates(self, x):
+        y, logdet = self.bn_arn(x)
+        return y, logdet
+
+    def inv(self, y):
+        raise RuntimeError("Block neural autoregressive transform does not have an analytic"
+                           " inverse implemented.")
+
+    def log_abs_det_jacobian(self, x, y, intermediates=None):
+        """
+        Calculates the elementwise determinant of the log jacobian.
 
-    def log_abs_det_jacobian(self, x, y, caching=True):
-        if caching:
-            return self._cached_logdet
+        :param numpy.ndarray x: the input to the transform
+        :param numpy.ndarray y: the output of the transform
+        """
+        if intermediates is None:
+            logdet = self.bn_arn(x)[1]
+            return logdet.sum(-1)
         else:
-            _, logdet = self.bna_nn(self.params, x)
-            return logdet
+            log_scale = intermediates
+            return log_scale.sum(-1)

From db797c44f81d9c962dd4dfc770edeaac4c082aae Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 00:44:20 -0400
Subject: [PATCH 26/35] updates nn for jax46

---
 numpyro/contrib/distributions/multivariate.py | 2 +-
 numpyro/contrib/nn/masked_dense.py            | 4 ++--
 numpyro/distributions/constraints.py          | 3 ++-
 numpyro/distributions/discrete.py             | 2 +-
 numpyro/distributions/util.py                 | 6 +-----
 5 files changed, 7 insertions(+), 10 deletions(-)

diff --git a/numpyro/contrib/distributions/multivariate.py b/numpyro/contrib/distributions/multivariate.py
index 510fdad6c..53ab63501 100644
--- a/numpyro/contrib/distributions/multivariate.py
+++ b/numpyro/contrib/distributions/multivariate.py
@@ -7,7 +7,7 @@
 # All rights reserved.
 
 from jax import lax, random
-from jax.experimental.stax import softmax
+from jax.nn import softmax
 import jax.numpy as np
 from jax.numpy.lax_numpy import _promote_dtypes
 from jax.scipy.special import digamma, entr, gammaln, logsumexp
diff --git a/numpyro/contrib/nn/masked_dense.py b/numpyro/contrib/nn/masked_dense.py
index a1593c319..11e0e5a56 100644
--- a/numpyro/contrib/nn/masked_dense.py
+++ b/numpyro/contrib/nn/masked_dense.py
@@ -1,9 +1,9 @@
 from jax import random
-from jax.experimental.stax import glorot, randn
+from jax.nn.initilizers import glorot_normal, normal
 import jax.numpy as np
 
 
-def MaskedDense(mask, bias=True, W_init=glorot(), b_init=randn()):
+def MaskedDense(mask, bias=True, W_init=glorot_normal(), b_init=normal()):
     """
     As in jax.experimental.stax, each layer constructor function returns
     an (init_fun, apply_fun) pair, where `init_fun` takes an rng key and
diff --git a/numpyro/distributions/constraints.py b/numpyro/distributions/constraints.py
index 190944835..1b6d92528 100644
--- a/numpyro/distributions/constraints.py
+++ b/numpyro/distributions/constraints.py
@@ -26,6 +26,7 @@
 
 from jax import ops
 from jax.lib.xla_bridge import canonicalize_dtype
+from jax.nn import softplus
 import jax.numpy as np
 from jax.scipy.special import expit, logit
 
@@ -361,7 +362,7 @@ def log_abs_det_jacobian(self, x, y, intermediates=None):
         z1m_cumprod_tril = matrix_to_tril_vec(z1m_cumprod, diagonal=-2)
         stick_breaking_logdet = 0.5 * np.sum(np.log(z1m_cumprod_tril), axis=-1)
 
-        tanh_logdet = -2 * np.sum(np.log(np.cosh(x)), axis=-1)
+        tanh_logdet = -2 * np.sum(x + softplus(-2 * x) - np.log(2.), axis=-1)
         return stick_breaking_logdet + tanh_logdet
 
 
diff --git a/numpyro/distributions/discrete.py b/numpyro/distributions/discrete.py
index c99a4654a..8194124ab 100644
--- a/numpyro/distributions/discrete.py
+++ b/numpyro/distributions/discrete.py
@@ -24,6 +24,7 @@
 
 from jax import lax
 from jax.lib import xla_bridge
+from jax.nn import softmax
 import jax.numpy as np
 import jax.random as random
 from jax.scipy.special import gammaln, logsumexp
@@ -40,7 +41,6 @@
     multinomial,
     poisson,
     promote_shapes,
-    softmax,
     sum_rightmost,
     xlog1py,
     xlogy
diff --git a/numpyro/distributions/util.py b/numpyro/distributions/util.py
index 540bb7314..439d92870 100644
--- a/numpyro/distributions/util.py
+++ b/numpyro/distributions/util.py
@@ -171,17 +171,13 @@ def cholesky_inverse(matrix):
     return solve_triangular(tril_inv, identity, lower=True)
 
 
+# TODO: move upstream to jax.nn
 def binary_cross_entropy_with_logits(x, y):
     # compute -y * log(sigmoid(x)) - (1 - y) * log(1 - sigmoid(x))
     # Ref: https://www.tensorflow.org/api_docs/python/tf/nn/sigmoid_cross_entropy_with_logits
     return np.clip(x, 0) + np.log1p(np.exp(-np.abs(x))) - x * y
 
 
-def softmax(x, axis=-1):
-    unnormalized = np.exp(x - np.max(x, axis, keepdims=True))
-    return unnormalized / np.sum(unnormalized, axis, keepdims=True)
-
-
 @custom_transforms
 def cumsum(x):
     return np.cumsum(x, axis=-1)

From 46faa8ea830575f9b2f4bc79cef15eee8edc1834 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 00:49:27 -0400
Subject: [PATCH 27/35] relax version restriction

---
 setup.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/setup.py b/setup.py
index 9a8d5df46..2fec477e8 100644
--- a/setup.py
+++ b/setup.py
@@ -31,8 +31,8 @@
     author_email='npradhan@uber.com',
     install_requires=[
         # TODO: pin to a specific version for the next release (unless JAX's API becomes stable)
-        'jax==0.1.44',
-        'jaxlib==0.1.27',
+        'jax>=0.1.44',
+        'jaxlib>=0.1.27',
         'tqdm',
     ],
     extras_require={

From 904adb8439c21455d232d0ed4b600c9119447591 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 00:53:47 -0400
Subject: [PATCH 28/35] change softmax import in ts notebook

---
 notebooks/source/time_series_forecasting.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/notebooks/source/time_series_forecasting.ipynb b/notebooks/source/time_series_forecasting.ipynb
index cc2d91c46..19903f3e3 100644
--- a/notebooks/source/time_series_forecasting.ipynb
+++ b/notebooks/source/time_series_forecasting.ipynb
@@ -32,14 +32,14 @@
     "import jax.numpy as np\n",
     "from jax import lax, random, vmap\n",
     "from jax.config import config; config.update(\"jax_platform_name\", \"cpu\")\n",
+    "from jax.nn import softmax\n",
     "\n",
     "import numpyro\n",
     "import numpyro.distributions as dist\n",
     "from numpyro.diagnostics import autocorrelation, hpdi\n",
-    "from numpyro.distributions.util import softmax\n",
     "from numpyro import handlers\n",
     "from numpyro.mcmc import MCMC, NUTS\n",
-    "assert numpyro.__version__.startswith('0.2.0')\n"
+    "assert numpyro.__version__.startswith('0.2.0')"
    ]
   },
   {

From 45c849cdf5ac3cf229f6701d8efaf774ae913c3a Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 10:00:36 -0400
Subject: [PATCH 29/35] make sure that mask_o is upper triangular matrix, not
 lower

---
 numpyro/contrib/nn/block_neural_arn.py  | 4 ++--
 test/contrib/test_auto_regressive_nn.py | 8 +++++++-
 test/test_distributions.py              | 2 +-
 test/test_flows.py                      | 6 +++++-
 4 files changed, 15 insertions(+), 5 deletions(-)

diff --git a/numpyro/contrib/nn/block_neural_arn.py b/numpyro/contrib/nn/block_neural_arn.py
index 743212aff..cd70755b1 100644
--- a/numpyro/contrib/nn/block_neural_arn.py
+++ b/numpyro/contrib/nn/block_neural_arn.py
@@ -23,8 +23,8 @@ def BlockMaskedDense(num_blocks, in_factor, out_factor, bias=True, W_init=glorot
     # Diagonal block mask
     mask_d = np.identity(num_blocks)[..., None]
     mask_d = np.tile(mask_d, (1, in_factor, out_factor)).reshape(input_dim, out_dim)
-    # Off-diagonal block mask for lower triangular weight matrix
-    mask_o = vec_to_tril_matrix(np.ones(num_blocks * (num_blocks - 1) // 2), diagonal=-1)[..., None]
+    # Off-diagonal block mask for upper triangular weight matrix
+    mask_o = vec_to_tril_matrix(np.ones(num_blocks * (num_blocks - 1) // 2), diagonal=-1).T[..., None]
     mask_o = np.tile(mask_o, (1, in_factor, out_factor)).reshape(input_dim, out_dim)
 
     def init_fun(rng, input_shape):
diff --git a/test/contrib/test_auto_regressive_nn.py b/test/contrib/test_auto_regressive_nn.py
index ea1a8fe4c..68ed877ad 100644
--- a/test/contrib/test_auto_regressive_nn.py
+++ b/test/contrib/test_auto_regressive_nn.py
@@ -9,6 +9,7 @@
 
 from numpyro.contrib.nn.auto_reg_nn import AutoregressiveNN, create_mask
 from numpyro.contrib.nn.block_neural_arn import BlockNeuralAutoregressiveNN
+from numpyro.distributions.util import matrix_to_tril_vec
 
 
 @pytest.mark.parametrize('input_dim', [5])
@@ -50,7 +51,8 @@ def test_auto_reg_nn(input_dim, hidden_dims, param_dims, skip_connections):
             permuted_jac[..., j, k] = jac[..., perm[j], perm[k]]
 
     # make sure jacobians are triangular
-    assert onp.sum(onp.abs(onp.triu(permuted_jac))) == 0.0
+    assert onp.sum(onp.abs(onp.triu(permuted_jac, k=1))) == 0.0
+    assert onp.all(onp.abs(matrix_to_tril_vec(jac)) > 0)
 
 
 @pytest.mark.parametrize('input_dim', [5, 8])
@@ -123,3 +125,7 @@ def test_block_neural_arn(input_dim, hidden_factors, residual, batch_shape):
     else:
         jac = jacfwd(lambda x: arn(init_params, x)[0])(x)
     assert_allclose(logdet.sum(-1), np.linalg.slogdet(jac)[1], rtol=1e-6)
+
+    # make sure jacobians are lower triangular
+    assert onp.sum(onp.abs(onp.triu(jac, k=1))) == 0.0
+    assert onp.all(onp.abs(matrix_to_tril_vec(jac)) > 0)
diff --git a/test/test_distributions.py b/test/test_distributions.py
index 6ec633a8a..4128cdb71 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -557,7 +557,7 @@ def test_distribution_constraints(jax_dist, sp_dist, params, prepend_shape):
             expected = sp_dist(*valid_params).logpdf(valid_samples)
         except AttributeError:
             expected = sp_dist(*valid_params).logpmf(valid_samples)
-        assert_allclose(d.log_prob(valid_samples), expected, atol=1e-5)
+        assert_allclose(d.log_prob(valid_samples), expected, atol=1e-5, rtol=1e-5)
 
     # Out of support samples throw ValueError
     oob_samples = gen_values_outside_bounds(d.support, size=prepend_shape + d.batch_shape + d.event_shape)
diff --git a/test/test_flows.py b/test/test_flows.py
index 219283e24..6c1dd569e 100644
--- a/test/test_flows.py
+++ b/test/test_flows.py
@@ -8,6 +8,7 @@
 
 from numpyro.contrib.nn import AutoregressiveNN, BlockNeuralAutoregressiveNN
 from numpyro.distributions.flows import BlockNeuralAutoregressiveTransform, InverseAutoregressiveTransform
+from numpyro.distributions.util import matrix_to_tril_vec
 
 
 def _make_iaf_args(input_dim, hidden_dims):
@@ -63,4 +64,7 @@ def test_flows(flow_class, flow_args, input_dim, batch_shape):
                 for k in range(input_dim):
                     permuted_jac[j, k] = jac[perm[j], perm[k]]
 
-            assert onp.sum(onp.abs(onp.triu(permuted_jac, 1))) == 0.00
+            jac = permuted_jac
+
+        assert onp.sum(onp.abs(onp.triu(jac, 1))) == 0.00
+        assert onp.all(onp.abs(matrix_to_tril_vec(jac)) > 0)

From 8f04ca3b040752135c81bbd3a6c081ea5b1439d9 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 13:31:14 -0400
Subject: [PATCH 30/35] use Elu for IAF

---
 test/test_flows.py | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/test/test_flows.py b/test/test_flows.py
index 6c1dd569e..847818837 100644
--- a/test/test_flows.py
+++ b/test/test_flows.py
@@ -5,6 +5,7 @@
 import pytest
 
 from jax import jacfwd, random
+from jax.experimental import stax
 
 from numpyro.contrib.nn import AutoregressiveNN, BlockNeuralAutoregressiveNN
 from numpyro.distributions.flows import BlockNeuralAutoregressiveTransform, InverseAutoregressiveTransform
@@ -14,7 +15,10 @@
 def _make_iaf_args(input_dim, hidden_dims):
     _, rng_perm = random.split(random.PRNGKey(0))
     perm = random.shuffle(rng_perm, onp.arange(input_dim))
-    arn_init, arn = AutoregressiveNN(input_dim, hidden_dims, param_dims=[1, 1], permutation=perm)
+    # we use Elu nonlinearity because the default one, Relu, masks out negative hidden values,
+    # which in turn create some zero entries in the lower triangular part of Jacobian.
+    arn_init, arn = AutoregressiveNN(input_dim, hidden_dims, param_dims=[1, 1],
+                                     permutation=perm, nonlinearity=stax.Elu)
     _, init_params = arn_init(random.PRNGKey(0), (input_dim,))
     return partial(arn, init_params),
 

From 0bc59d1f7f4ef596a4c8987783c3b3f6d08736cd Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 13:33:22 -0400
Subject: [PATCH 31/35] revert arn test

---
 test/contrib/test_auto_regressive_nn.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/test/contrib/test_auto_regressive_nn.py b/test/contrib/test_auto_regressive_nn.py
index 68ed877ad..1116b8a42 100644
--- a/test/contrib/test_auto_regressive_nn.py
+++ b/test/contrib/test_auto_regressive_nn.py
@@ -51,8 +51,7 @@ def test_auto_reg_nn(input_dim, hidden_dims, param_dims, skip_connections):
             permuted_jac[..., j, k] = jac[..., perm[j], perm[k]]
 
     # make sure jacobians are triangular
-    assert onp.sum(onp.abs(onp.triu(permuted_jac, k=1))) == 0.0
-    assert onp.all(onp.abs(matrix_to_tril_vec(jac)) > 0)
+    assert onp.sum(onp.abs(onp.triu(permuted_jac))) == 0.0
 
 
 @pytest.mark.parametrize('input_dim', [5, 8])

From deeee196d2233022e94c209ba2f4664e206f9045 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 14:00:14 -0400
Subject: [PATCH 32/35] add bnaf autoguide

---
 numpyro/contrib/autoguide/__init__.py | 59 ++++++++++++++++++++++++---
 test/contrib/test_autoguide.py        | 27 ++++++------
 2 files changed, 68 insertions(+), 18 deletions(-)

diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index aa82e9081..ff0a7ccfd 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -10,10 +10,11 @@
 import numpyro
 from numpyro import handlers
 from numpyro.contrib.nn.auto_reg_nn import AutoregressiveNN
+from numpyro.contrib.nn.block_neural_arn import BlockNeuralAutoregressiveNN
 import numpyro.distributions as dist
 from numpyro.distributions import constraints
 from numpyro.distributions.constraints import AffineTransform, ComposeTransform, PermuteTransform, biject_to
-from numpyro.distributions.flows import InverseAutoregressiveTransform
+from numpyro.distributions.flows import BlockNeuralAutoregressiveTransform, InverseAutoregressiveTransform
 from numpyro.distributions.util import sum_rightmost
 from numpyro.infer_util import constrain_fn, find_valid_initial_params, init_to_median, transform_fn
 
@@ -112,9 +113,9 @@ def _setup_prototype(self, *args, **kwargs):
         super(AutoContinuous, self)._setup_prototype(*args, **kwargs)
         rng = numpyro.sample("_{}_rng_init".format(self.prefix), dist.PRNGIdentity())
         # FIXME: without block statement, get AssertionError: all sites must have unique names
-        init_params, is_valid = handlers.block(find_valid_initial_params)(rng, self.model, *args,
-                                                                          init_strategy=self.init_strategy,
-                                                                          **kwargs)
+        init_params, _ = handlers.block(find_valid_initial_params)(rng, self.model, *args,
+                                                                   init_strategy=self.init_strategy,
+                                                                   **kwargs)
         self._inv_transforms = {}
         self._has_transformed_dist = False
         unconstrained_sites = {}
@@ -315,7 +316,7 @@ class AutoIAFNormal(AutoContinuous):
     Usage::
 
         guide = AutoIAFNormal(rng, model, get_params, hidden_dims=[20], skip_connections=True, ...)
-        svi_init, svi_update, _ = svi(model, guide, ...)
+        svi = SVI(model, guide, ...)
 
     :param jax.random.PRNGKey rng: random key to be used as the source of randomness
         to initialize the guide.
@@ -360,3 +361,51 @@ def _get_transform(self):
             arnn = numpyro.module('{}_arn__{}'.format(self.prefix, i), arn, (self.latent_size,))
             flows.append(InverseAutoregressiveTransform(arnn))
         return ComposeTransform(flows)
+
+
+class AutoBNAFNormal(AutoContinuous):
+    """
+    This implementation of :class:`AutoContinuous` uses a Diagonal Normal
+    distribution transformed via a
+    :class:`~numpyro.distributions.iaf.InverseAutoregressiveTransform`
+    to construct a guide over the entire latent space. The guide does not
+    depend on the model's ``*args, **kwargs``.
+
+    Usage::
+
+        guide = AutoBNAFNormal(rng, model, get_params, num_flows=1, hidden_factors=[50, 50])
+        svi = SVI(model, guide, ...)
+
+    **References**
+
+    1. *Block Neural Autoregressive Flow*,
+       Nicola De Cao, Ivan Titov, Wilker Aziz
+
+    :param jax.random.PRNGKey rng: random key to be used as the source of randomness
+        to initialize the guide.
+    :param callable model: a generative model.
+    :param str prefix: a prefix that will be prefixed to all param internal sites.
+    :param callable init_strategy: A per-site initialization function.
+    :param int num_flows: the number of flows to be used, defaults to 3.
+    :param list hidden_factors: Hidden layer i has ``hidden_factors[i]`` hidden units per
+        input dimension. This corresponds to both :math:`a` and :math:`b` in reference [1].
+        The elements of hidden_factors must be integers.
+    """
+    def __init__(self, model, prefix="auto", init_strategy=init_to_median, num_flows=1,
+                 hidden_factors=[8, 8]):
+        self.num_flows = num_flows
+        self._hidden_factors = hidden_factors
+        super(AutoBNAFNormal, self).__init__(model, prefix=prefix, init_strategy=init_strategy)
+
+    def _get_transform(self):
+        if self.latent_size == 1:
+            raise ValueError('latent dim = 1. Consider using AutoDiagonalNormal instead')
+        flows = []
+        for i in range(self.num_flows):
+            if i > 0:
+                flows.append(PermuteTransform(np.arange(self.latent_size)[::-1]))
+            residual = "gated" if i < (self.num_flows - 1) else None
+            arn = BlockNeuralAutoregressiveNN(self.latent_size, self._hidden_factors, residual)
+            arnn = numpyro.module('{}_arn__{}'.format(self.prefix, i), arn, (self.latent_size,))
+            flows.append(BlockNeuralAutoregressiveTransform(arnn))
+        return ComposeTransform(flows)
diff --git a/test/contrib/test_autoguide.py b/test/contrib/test_autoguide.py
index 30b1b6460..d0bc0ce8e 100644
--- a/test/contrib/test_autoguide.py
+++ b/test/contrib/test_autoguide.py
@@ -9,7 +9,7 @@
 
 import numpyro
 from numpyro import optim
-from numpyro.contrib.autoguide import AutoDiagonalNormal, AutoIAFNormal
+from numpyro.contrib.autoguide import AutoBNAFNormal, AutoDiagonalNormal, AutoIAFNormal
 from numpyro.contrib.nn.auto_reg_nn import AutoregressiveNN
 import numpyro.distributions as dist
 from numpyro.distributions import constraints
@@ -22,6 +22,7 @@
 @pytest.mark.parametrize('auto_class', [
     AutoDiagonalNormal,
     AutoIAFNormal,
+    AutoBNAFNormal,
 ])
 def test_beta_bernoulli(auto_class):
     data = np.array([[1.0] * 8 + [0.0] * 2,
@@ -32,15 +33,15 @@ def model(data):
         numpyro.sample('obs', dist.Bernoulli(f), obs=data)
 
     adam = optim.Adam(0.01)
-    guide = auto_class(model)
+    guide = auto_class(model, hidden_factors=[8, 8]) if auto_class is AutoBNAFNormal else auto_class(model)
     svi = SVI(model, guide, elbo, adam)
     svi_state = svi.init(random.PRNGKey(1), model_args=(data,), guide_args=(data,))
 
     def body_fn(i, val):
-        svi_state, loss = svi.update(val, model_args=(data,), guide_args=(data,))
+        svi_state, _ = svi.update(val, model_args=(data,), guide_args=(data,))
         return svi_state
 
-    svi_state = fori_loop(0, 2000, body_fn, svi_state)
+    svi_state = fori_loop(0, 3000, body_fn, svi_state)
     params = svi.get_params(svi_state)
     true_coefs = (np.sum(data, axis=0) + 1) / (data.shape[0] + 2)
     # test .sample_posterior method
@@ -51,6 +52,7 @@ def body_fn(i, val):
 @pytest.mark.parametrize('auto_class', [
     AutoDiagonalNormal,
     AutoIAFNormal,
+    AutoBNAFNormal,
 ])
 def test_logistic_regression(auto_class):
     N, dim = 3000, 3
@@ -71,12 +73,12 @@ def model(data, labels):
     svi_state = svi.init(rng_init, model_args=(data, labels), guide_args=(data, labels))
 
     def body_fn(i, val):
-        svi_state, loss = svi.update(val, model_args=(data, labels), guide_args=(data, labels))
+        svi_state, _ = svi.update(val, model_args=(data, labels), guide_args=(data, labels))
         return svi_state
 
     svi_state = fori_loop(0, 2000, body_fn, svi_state)
     params = svi.get_params(svi_state)
-    if auto_class is not AutoIAFNormal:
+    if auto_class not in (AutoIAFNormal, AutoBNAFNormal):
         median = guide.median(params)
         assert_allclose(median['coefs'], true_coefs, rtol=0.1)
         # test .quantile method
@@ -117,16 +119,15 @@ def model(data, labels):
     for i in range(guide.num_flows):
         if i > 0:
             flows.append(constraints.PermuteTransform(np.arange(dim + 1)[::-1]))
-        arn_init, arn_apply = AutoregressiveNN(dim + 1, [dim + 1, dim + 1],
-                                               permutation=np.arange(dim + 1),
-                                               skip_connections=guide._skip_connections,
-                                               nonlinearity=guide._nonlinearity)
+        _, arn_apply = AutoregressiveNN(dim + 1, [dim + 1, dim + 1],
+                                        permutation=np.arange(dim + 1),
+                                        skip_connections=guide._skip_connections,
+                                        nonlinearity=guide._nonlinearity)
         arn = partial(arn_apply, params['auto_arn__{}$params'.format(i)])
         flows.append(InverseAutoregressiveTransform(arn))
 
     transform = constraints.ComposeTransform(flows)
-    rng_seed, rng_sample = random.split(rng)
-    expected_sample = guide.unpack_latent(transform(dist.Normal(np.zeros(dim + 1), 1).sample(rng_sample)))
+    expected_sample = guide.unpack_latent(transform(dist.Normal(np.zeros(dim + 1), 1).sample(rng)))
     expected_output = transform(x)
     assert_allclose(actual_sample['coefs'], expected_sample['coefs'])
     assert_allclose(actual_sample['offset'],
@@ -150,7 +151,7 @@ def model(data):
     svi_state = svi.init(rng_init, model_args=(data,), guide_args=(data,))
 
     def body_fn(i, val):
-        svi_state, loss = svi.update(val, model_args=(data,), guide_args=(data,))
+        svi_state, _ = svi.update(val, model_args=(data,), guide_args=(data,))
         return svi_state
 
     svi_state = fori_loop(0, 1000, body_fn, svi_state)

From 38add0acef07746f61c3fe41f3648391310628fa Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 15:16:01 -0400
Subject: [PATCH 33/35] use bnaf in neutra

---
 examples/neutra.py | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

diff --git a/examples/neutra.py b/examples/neutra.py
index a9bd5e244..b900eb1a1 100644
--- a/examples/neutra.py
+++ b/examples/neutra.py
@@ -13,7 +13,7 @@
 
 import numpyro
 from numpyro import optim
-from numpyro.contrib.autoguide import AutoIAFNormal
+from numpyro.contrib.autoguide import AutoBNAFNormal
 from numpyro.diagnostics import summary
 import numpyro.distributions as dist
 from numpyro.hmc_util import initialize_model
@@ -40,7 +40,7 @@ def dual_moon_pe(x):
 
 
 def dual_moon_model():
-    x = numpyro.sample('x', dist.Uniform(-4 * np.ones(2), 4 * np.ones(2)))
+    x = numpyro.sample('x', dist.Normal(np.zeros(2), 100))
     pe = dual_moon_pe(x)
     numpyro.sample('log_density', dist.Delta(log_density=-pe), obs=0.)
 
@@ -63,9 +63,9 @@ def main(args):
     mcmc.run(random.PRNGKey(11), init_params=np.array([2., 0.]))
     vanilla_samples = mcmc.get_samples()
 
-    adam = optim.Adam(0.001)
+    adam = optim.Adam(0.01)
     rng_init, rng_train = random.split(random.PRNGKey(1), 2)
-    guide = AutoIAFNormal(dual_moon_model, hidden_dims=[args.num_hidden], skip_connections=True)
+    guide = AutoBNAFNormal(dual_moon_model, hidden_factors=[50, 50])
     svi = SVI(dual_moon_model, guide, elbo, adam)
     svi_state = svi.init(rng_init)
 
@@ -89,10 +89,12 @@ def main(args):
     # Issue: https://github.com/pyro-ppl/numpyro/issues/256
     nuts_kernel = NUTS(potential_fn=transformed_potential_fn)
     mcmc = MCMC(nuts_kernel, args.num_warmup, args.num_samples)
-    mcmc.run(random.PRNGKey(10), init_params=init_params)
+    mcmc.run(random.PRNGKey(10), init_params=init_params, collect_fields=('z', 'potential_energy'))
     zs = mcmc.get_samples()
+    print(zs)
     print("Transform samples into unwarped space...")
     samples = vmap(transformed_constrain_fn)(zs)
+    print(samples)
     summary(tree_map(lambda x: x[None, ...], samples))
 
     # make plots
@@ -151,10 +153,10 @@ def main(args):
 if __name__ == "__main__":
     assert numpyro.__version__.startswith('0.2.0')
     parser = argparse.ArgumentParser(description="NeuTra HMC")
-    parser.add_argument('-n', '--num-samples', nargs='?', default=20000, type=int)
-    parser.add_argument('--num-warmup', nargs='?', default=0, type=int)
+    parser.add_argument('-n', '--num-samples', nargs='?', default=5000, type=int)
+    parser.add_argument('--num-warmup', nargs='?', default=5000, type=int)
     parser.add_argument('--num-hidden', nargs='?', default=20, type=int)
-    parser.add_argument('--num-iters', nargs='?', default=200000, type=int)
+    parser.add_argument('--num-iters', nargs='?', default=20000, type=int)
     parser.add_argument('--device', default='cpu', type=str, help='use "cpu" or "gpu".')
     args = parser.parse_args()
     main(args)

From 952e8ef3c4db36617b8e4ad248891abb0c7ed03e Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 18 Sep 2019 23:03:44 -0400
Subject: [PATCH 34/35] finalllygit add -u .git add -u .! neutra example works

---
 examples/neutra.py                    | 60 ++++++++++++---------------
 numpyro/contrib/autoguide/__init__.py |  2 +-
 2 files changed, 27 insertions(+), 35 deletions(-)

diff --git a/examples/neutra.py b/examples/neutra.py
index b900eb1a1..707c47c5b 100644
--- a/examples/neutra.py
+++ b/examples/neutra.py
@@ -1,5 +1,4 @@
 import argparse
-import os
 
 from matplotlib.gridspec import GridSpec
 import matplotlib.pyplot as plt
@@ -20,10 +19,6 @@
 from numpyro.mcmc import MCMC, NUTS
 from numpyro.svi import SVI, elbo
 
-# TODO: remove when the issue https://github.com/google/jax/issues/939 is fixed upstream
-# The behaviour when training guide under fast math mode is unstable.
-os.environ["XLA_FLAGS"] = "--xla_cpu_enable_fast_math=false"
-
 """
 This example illustrates how to use a trained AutoIAFNormal autoguide to transform a posterior to a
 Gaussian-like one. The transform will be used to get better mixing rate for NUTS sampler.
@@ -49,7 +44,7 @@ def make_transformed_pe(potential_fn, transform, unpack_fn):
     def transformed_potential_fn(z):
         u, intermediates = transform.call_with_intermediates(z)
         logdet = transform.log_abs_det_jacobian(z, u, intermediates=intermediates)
-        return potential_fn(unpack_fn(u)) + logdet
+        return potential_fn(unpack_fn(u)) - logdet
 
     return transformed_potential_fn
 
@@ -58,23 +53,23 @@ def main(args):
     jax_config.update('jax_platform_name', args.device)
 
     print("Start vanilla HMC...")
-    nuts_kernel = NUTS(potential_fn=dual_moon_pe)
+    nuts_kernel = NUTS(dual_moon_model)
     mcmc = MCMC(nuts_kernel, args.num_warmup, args.num_samples)
-    mcmc.run(random.PRNGKey(11), init_params=np.array([2., 0.]))
-    vanilla_samples = mcmc.get_samples()
+    mcmc.run(random.PRNGKey(0))
+    mcmc.print_summary()
+    vanilla_samples = mcmc.get_samples()['x'].copy()
 
     adam = optim.Adam(0.01)
-    rng_init, rng_train = random.split(random.PRNGKey(1), 2)
-    guide = AutoBNAFNormal(dual_moon_model, hidden_factors=[50, 50])
+    guide = AutoBNAFNormal(dual_moon_model, hidden_factors=[args.hidden_factor, args.hidden_factor])
     svi = SVI(dual_moon_model, guide, elbo, adam)
-    svi_state = svi.init(rng_init)
+    svi_state = svi.init(random.PRNGKey(1))
 
     print("Start training guide...")
     last_state, losses = lax.scan(lambda state, i: svi.update(state), svi_state, np.zeros(args.num_iters))
     params = svi.get_params(last_state)
     print("Finish training guide. Extract samples...")
     guide_samples = guide.sample_posterior(random.PRNGKey(0), params,
-                                           sample_shape=(args.num_samples,))
+                                           sample_shape=(args.num_samples,))['x'].copy()
 
     transform = guide.get_transform(params)
     unpack_fn = guide.unpack_latent
@@ -83,25 +78,22 @@ def main(args):
     transformed_potential_fn = make_transformed_pe(potential_fn, transform, unpack_fn)
     transformed_constrain_fn = lambda x: constrain_fn(unpack_fn(transform(x)))  # noqa: E731
 
-    init_params = np.zeros(guide.latent_size)
     print("\nStart NeuTra HMC...")
-    # TODO: exlore why neutra samples are not good
-    # Issue: https://github.com/pyro-ppl/numpyro/issues/256
     nuts_kernel = NUTS(potential_fn=transformed_potential_fn)
     mcmc = MCMC(nuts_kernel, args.num_warmup, args.num_samples)
-    mcmc.run(random.PRNGKey(10), init_params=init_params, collect_fields=('z', 'potential_energy'))
+    init_params = np.zeros(guide.latent_size)
+    mcmc.run(random.PRNGKey(2), init_params=init_params)
+    mcmc.print_summary()
     zs = mcmc.get_samples()
-    print(zs)
     print("Transform samples into unwarped space...")
-    samples = vmap(transformed_constrain_fn)(zs)
-    print(samples)
+    samples = vmap(transformed_constrain_fn)(zs)['x'].copy()
     summary(tree_map(lambda x: x[None, ...], samples))
 
     # make plots
 
-    # IAF guide samples (for plotting)
-    iaf_base_samples = dist.Normal(np.zeros(2), 1.).sample(random.PRNGKey(0), (1000,))
-    iaf_trans_samples = vmap(transformed_constrain_fn)(iaf_base_samples)['x']
+    # BNAF guide samples (for plotting)
+    bnaf_base_samples = dist.Normal(np.zeros(2), 1.).sample(random.PRNGKey(0), (1000,))
+    bnaf_trans_samples = vmap(transformed_constrain_fn)(bnaf_base_samples)['x']
 
     x1 = np.linspace(-3, 3, 100)
     x2 = np.linspace(-3, 3, 100)
@@ -121,28 +113,28 @@ def main(args):
     ax1.set_title('Autoguide training log loss (after 1000 steps)')
 
     ax2.contourf(X1, X2, P, cmap='OrRd')
-    sns.kdeplot(guide_samples['x'][:, 0].copy(), guide_samples['x'][:, 1].copy(), n_levels=30, ax=ax2)
+    sns.kdeplot(guide_samples[:, 0], guide_samples[:, 1], n_levels=30, ax=ax2)
     ax2.set(xlim=[-3, 3], ylim=[-3, 3],
-            xlabel='x0', ylabel='x1', title='Posterior using AutoIAFNormal guide')
+            xlabel='x0', ylabel='x1', title='Posterior using AutoBNAFNormal guide')
 
-    sns.scatterplot(iaf_base_samples[:, 0], iaf_base_samples[:, 1], ax=ax3, hue=iaf_trans_samples[:, 0] < 0.)
+    sns.scatterplot(bnaf_base_samples[:, 0], bnaf_base_samples[:, 1], ax=ax3, hue=bnaf_trans_samples[:, 0] < 0.)
     ax3.set(xlim=[-3, 3], ylim=[-3, 3],
-            xlabel='x0', ylabel='x1', title='AutoIAFNormal base samples (True=left moon; False=right moon)')
+            xlabel='x0', ylabel='x1', title='AutoBNAFNormal base samples (True=left moon; False=right moon)')
 
     ax4.contourf(X1, X2, P, cmap='OrRd')
-    sns.kdeplot(vanilla_samples[:, 0].copy(), vanilla_samples[:, 1].copy(), n_levels=30, ax=ax4)
+    sns.kdeplot(vanilla_samples[:, 0], vanilla_samples[:, 1], n_levels=30, ax=ax4)
     ax4.plot(vanilla_samples[-50:, 0], vanilla_samples[-50:, 1], 'bo-', alpha=0.5)
     ax4.set(xlim=[-3, 3], ylim=[-3, 3],
             xlabel='x0', ylabel='x1', title='Posterior using vanilla HMC sampler')
 
-    sns.scatterplot(zs[:, 0], zs[:, 1], ax=ax5, hue=samples['x'][:, 0] < 0.,
+    sns.scatterplot(zs[:, 0], zs[:, 1], ax=ax5, hue=samples[:, 0] < 0.,
                     s=30, alpha=0.5, edgecolor="none")
     ax5.set(xlim=[-5, 5], ylim=[-5, 5],
             xlabel='x0', ylabel='x1', title='Samples from the warped posterior - p(z)')
 
     ax6.contourf(X1, X2, P, cmap='OrRd')
-    sns.kdeplot(samples['x'][:, 0].copy(), samples['x'][:, 1].copy(), n_levels=30, ax=ax6)
-    ax6.plot(samples['x'][-50:, 0], samples['x'][-50:, 1], 'bo-', alpha=0.2)
+    sns.kdeplot(samples[:, 0], samples[:, 1], n_levels=30, ax=ax6)
+    ax6.plot(samples[-50:, 0], samples[-50:, 1], 'bo-', alpha=0.2)
     ax6.set(xlim=[-3, 3], ylim=[-3, 3],
             xlabel='x0', ylabel='x1', title='Posterior using NeuTra HMC sampler')
 
@@ -153,9 +145,9 @@ def main(args):
 if __name__ == "__main__":
     assert numpyro.__version__.startswith('0.2.0')
     parser = argparse.ArgumentParser(description="NeuTra HMC")
-    parser.add_argument('-n', '--num-samples', nargs='?', default=5000, type=int)
-    parser.add_argument('--num-warmup', nargs='?', default=5000, type=int)
-    parser.add_argument('--num-hidden', nargs='?', default=20, type=int)
+    parser.add_argument('-n', '--num-samples', nargs='?', default=10000, type=int)
+    parser.add_argument('--num-warmup', nargs='?', default=1000, type=int)
+    parser.add_argument('--hidden-factor', nargs='?', default=50, type=int)
     parser.add_argument('--num-iters', nargs='?', default=20000, type=int)
     parser.add_argument('--device', default='cpu', type=str, help='use "cpu" or "gpu".')
     args = parser.parse_args()
diff --git a/numpyro/contrib/autoguide/__init__.py b/numpyro/contrib/autoguide/__init__.py
index ff0a7ccfd..8957654e5 100644
--- a/numpyro/contrib/autoguide/__init__.py
+++ b/numpyro/contrib/autoguide/__init__.py
@@ -392,7 +392,7 @@ class AutoBNAFNormal(AutoContinuous):
         The elements of hidden_factors must be integers.
     """
     def __init__(self, model, prefix="auto", init_strategy=init_to_median, num_flows=1,
-                 hidden_factors=[8, 8]):
+                 hidden_factors=[50, 50]):
         self.num_flows = num_flows
         self._hidden_factors = hidden_factors
         super(AutoBNAFNormal, self).__init__(model, prefix=prefix, init_strategy=init_strategy)

From 866ce179dcc2201aef3fe384b6fe2356e02a6fa8 Mon Sep 17 00:00:00 2001
From: fehiepsi <fehiepsi@gmail.com>
Date: Wed, 25 Sep 2019 23:42:07 -0400
Subject: [PATCH 35/35] fix typo

---
 examples/neutra.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/neutra.py b/examples/neutra.py
index dbf37868e..803a0d19c 100644
--- a/examples/neutra.py
+++ b/examples/neutra.py
@@ -87,7 +87,7 @@ def main(args):
     mcmc.print_summary()
     zs = mcmc.get_samples()
     print("Transform samples into unwarped space...")
-    samples = vmap(transformed_constrain_fn)(zs)['x'].copy()
+    samples = vmap(transformed_constrain_fn)(zs)
     summary(tree_map(lambda x: x[None, ...], samples))
     samples = samples['x'].copy()