Create _make_halfnormal_prior function and change to priors on standard deviations

EpiAware/docs/src/examples/getting_started.jl

@@ -89,14 +89,14 @@ In `EpiAware` we provide a constructor for random walk latent models with priors
 ```math
 \begin{align}
 Z_0 &\sim \mathcal{N}(0,1),\\
-\sigma^2_Z &\sim \text{HalfNormal}(0.01).
+\sigma_{RW} &\sim \text{HalfNormal}(0.1 * \sqrt{\pi} / \sqrt{2})).
 \end{align}
 ```
 "
 
 # ╔═╡ 56ae496b-0094-460b-89cb-526627991717
 rwp = EpiAware.RandomWalk(Normal(),
-    truncated(Normal(0.0, 0.02), 0.0, Inf))
+    EpiAware._make_halfnormal_prior(0.1))
 
 # ╔═╡ 767beffd-1ef5-4e6c-9ac6-edb52e60fb44
 md"
@@ -179,7 +179,7 @@ We choose a simple observation model where infections are observed 0, 1, 2, 3 da
 obs_model = EpiAware.DelayObservations(
     fill(0.25, 4),
     time_horizon,
-    truncated(Normal(0, 0.1 * sqrt(pi) / sqrt(2)), 0.0, Inf)
+    EpiAware._make_halfnormal_prior(0.1)
 )
 
 # ╔═╡ e49713e8-4840-4083-8e3f-fc52d791be7b
@@ -298,12 +298,15 @@ init_params = collect.(eachrow(best_pf.draws_transformed.value[1:4, :, 1]))
 
 # ╔═╡ 4deb3a51-781d-48c4-91f6-6adf2b1affcf
 md"
-**NB: We are running this inference run for speed rather than accuracy as a demonstration. Use a higher target acceptance and more samples in a typical workflow.**
+**NB: We are running this inference run for speed rather than accuracy as a demonstration. You might want to use a higher target acceptance and more samples in a typical workflow.**
 "
 
+# ╔═╡ 946b1c43-e750-40c9-9f14-79da9735e437
+target_acc_prob = 0.8
+
 # ╔═╡ 3eb5ec5e-aae7-478e-84fb-80f2e9f85b4c
 chn = sample(inference_mdl,
-    NUTS(; adtype = AutoReverseDiff(true)),
+    NUTS(target_acc_prob; adtype = AutoReverseDiff(true)),
     MCMCThreads(),
     250,
     4;
@@ -360,7 +363,7 @@ As well as checking the posterior predictions for latent infections, we can also
 
 # ╔═╡ 10d8fe24-83a6-47ac-97b7-a374481473d3
 let
-    parameters_to_plot = (:σ²_RW, :neg_bin_cluster_factor)
+    parameters_to_plot = (:σ_RW, :neg_bin_cluster_factor)
 
     plts = map(parameters_to_plot) do name
         var_samples = chn[name] |> vec
@@ -446,10 +449,11 @@ end
 # ╠═b4033728-b321-4100-8194-1fd9fe2d268d
 # ╟─9222b436-9445-4039-abbf-25c8cddb7f63
 # ╠═197a4fbb-b71a-475a-bb78-28ff613e3094
-# ╠═073a1d40-456a-450e-969f-11b23eb7fd1f
+# ╟─073a1d40-456a-450e-969f-11b23eb7fd1f
 # ╠═0379b058-4c35-440a-bc01-aafa0178bdbf
 # ╠═a7798f71-9bb5-4506-9476-0cc11553b9e2
 # ╟─4deb3a51-781d-48c4-91f6-6adf2b1affcf
+# ╠═946b1c43-e750-40c9-9f14-79da9735e437
 # ╠═3eb5ec5e-aae7-478e-84fb-80f2e9f85b4c
 # ╟─30498cc7-16a5-441a-b8cd-c19b220c60c1
 # ╠═e9df22b8-8e4d-4ab7-91ea-c01f2239b3e5

EpiAware/src/latentmodels/randomwalk.jl

@@ -1,6 +1,6 @@
 struct RandomWalk{D <: Sampleable, S <: Sampleable} <: AbstractLatentModel
     init_prior::D
-    var_prior::S
+    std_prior::S
 end
 
 function default_rw_priors()
@@ -10,9 +10,8 @@ end
 
 @model function generate_latent(latent_model::RandomWalk, n)
     ϵ_t ~ MvNormal(ones(n))
-    σ²_RW ~ latent_model.var_prior
+    σ_RW ~ latent_model.std_prior
     rw_init ~ latent_model.init_prior
-    σ_RW = sqrt(σ²_RW)
     rw = Vector{eltype(ϵ_t)}(undef, n)
 
     rw[1] = rw_init + σ_RW * ϵ_t[1]

EpiAware/src/utils/dist.jl

@@ -150,8 +150,6 @@ function r_to_R(r, w::AbstractVector)
 end
 
 """
-    NegativeBinomialMeanClust(μ, α)
-
 Compute the mean-cluster factor negative binomial distribution.
 
 # Arguments
@@ -167,3 +165,17 @@ function NegativeBinomialMeanClust(μ, α)
     r = μ^2 / ex_σ²
     return NegativeBinomial(r, p)
 end
+
+"""
+Create a half-normal prior distribution with the specified mean.
+
+# Arguments
+- `prior_mean::AbstractFloat`: The mean of the prior distribution.
+
+# Returns
+- `Truncated{Normal}`: The half-normal prior distribution.
+
+"""
+function _make_halfnormal_prior(prior_mean::AbstractFloat)
+    return truncated(Normal(0.0, prior_mean * sqrt(pi) / sqrt(2)), 0.0, Inf)
+end

EpiAware/test/test_latent-models.jl

@@ -8,7 +8,7 @@
     rw_process = EpiAware.RandomWalk(Normal(0.0, 1.0),
         truncated(Normal(0.0, 0.05), 0.0, Inf))
     model = EpiAware.generate_latent(rw_process, n)
-    fixed_model = fix(model, (σ²_RW = 1.0, init_rw_value = 0.0)) #Fixing the standard deviation of the random walk process
+    fixed_model = fix(model, (σ_RW = 1.0, init_rw_value = 0.0)) #Fixing the standard deviation of the random walk process
     n_samples = 1000
     samples_day_5 = sample(fixed_model, Prior(), n_samples) |>
                     chn -> mapreduce(vcat, generated_quantities(fixed_model, chn)) do gen
@@ -33,8 +33,8 @@ end
 end
 @testset "Testing RandomWalk constructor" begin
     init_prior = Normal(0.0, 1.0)
-    var_prior = truncated(Normal(0.0, 0.05), 0.0, Inf)
-    rw_process = RandomWalk(init_prior, var_prior)
+    std_prior = truncated(Normal(0.0, 0.05), 0.0, Inf)
+    rw_process = RandomWalk(init_prior, std_prior)
     @test rw_process.init_prior == init_prior
-    @test rw_process.var_prior == var_prior
+    @test rw_process.std_prior == std_prior
 end

EpiAware/test/test_observation-models.jl

@@ -1,6 +1,6 @@
 @testitem "Testing delay obs against theoretical properties" begin
     using DynamicPPL, Turing, Distributions
-    using HypothesisTests#: ExactOneSampleKSTest, pvalue
+    using HypothesisTests
 
     # Set up test data with fixed infection
     I_t = [10.0, 20.0, 30.0]

EpiAware/test/test_utilities.jl

@@ -196,3 +196,26 @@ end
         @test df == expected_df
     end
 end
+
+@testitem "Testing _make_halfnormal_prior" begin
+    using Distributions, HypothesisTests
+    @testset "Check distribution type" begin
+        prior_mean = 10.0
+        prior_dist = EpiAware._make_halfnormal_prior(prior_mean)
+        @test typeof(prior_dist) <: Distribution
+    end
+
+    @testset "Check distribution properties" begin
+        prior_mean = 2.0
+        prior_dist = EpiAware._make_halfnormal_prior(prior_mean)
+        #Check Distributions.jl mean function
+        @test mean(prior_dist) ≈ prior_mean
+        samples = rand(prior_dist, 10_000)
+        #Check mean from direct sampling of folded distribution and ANOVA and Variance F test comparisons
+        direct_samples = randn(10_000) * prior_mean * sqrt(pi) / sqrt(2) .|> abs
+        mean_pval = OneWayANOVATest(samples, direct_samples) |> pvalue
+        @test mean_pval > 1e-6 #Very unlikely to fail if the model is correctly implemented
+        var_pval = VarianceFTest(samples, direct_samples) |> pvalue
+        @test var_pval > 1e-6 #Very unlikely to fail if the model is correctly implemented
+    end
+end