fix errors in pymc sampler implementaton

[felixp8]

What does this implement/fix? Explain your changes

Two errors in PyMCSampler fixed here:

• check for whether gradient tracking needed in line 141 of sbi.samplers.mcmc.pymc_wrapper looked for matching step class instead of the string value actually used and expected
• pymc.Model() incorrectly set up using a prior distribution and additional likelihood term which does not result in the desired distribution. Now using pymc.DensityDist which directly defines the distribution using given potential function
  With these changes test_c2st_pymc_sampler_on_Gaussian passes locally for all sampling methods.

Does this close any currently open issues?

Fixes #1127

Checklist

Put an x in the boxes that apply. You can also fill these out after creating
the PR. If you're unsure about any of them, don't hesitate to ask. We're here to
help! This is simply a reminder of what we are going to look for before merging
your code.

• I have read and understood the contribution
  guidelines
• I agree with re-licensing my contribution from AGPLv3 to Apache-2.0.
• I have commented my code, particularly in hard-to-understand areas
• I have added tests that prove my fix is effective or that my feature works
• I have reported how long the new tests run and potentially marked them
  with pytest.mark.slow.
• New and existing unit tests pass locally with my changes
• I performed linting and formatting as described in the contribution
  guidelines
• I rebased on main (or there are no conflicts with main)

[janfb]

Great! It seems that this fixes all the problems? (see https://github.com/sbi-dev/sbi/actions/runs/8597285263/job/23555649100#step:7:3794)

@felixp8 can you please rebase on main to include the recent fixes to the MCMC kwargs?

[felixp8]

yup will try to do by eod

[janfb]

After rebasing on main:

With your fixes, the slice and nuts samplers are working fine on the more difficult test. However, hmc is still failing and fluctuates with c2sts around 0.6.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 85.26%. Comparing base (7be2115) to head (b8d4ab5).
Report is 11 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1129      +/-   ##
==========================================
- Coverage   85.45%   85.26%   -0.19%     
==========================================
  Files          90       89       -1     
  Lines        6612     6616       +4     
==========================================
- Hits         5650     5641       -9     
- Misses        962      975      +13     

Flag	Coverage Δ
unittests	85.26% <100.00%> (-0.19%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files	Coverage Δ
sbi/samplers/mcmc/pymc_wrapper.py	88.40% <100.00%> (ø)

[felixp8]

darn okay I'm somewhat sure model log-probs are correct now but it's possible also that the gradient is not correct. Don't think I'll have time to carefully go through the pymc internals for that until later this week

[janfb]

darn okay I'm somewhat sure model log-probs are correct now but it's possible also that the gradient is not correct. Don't think I'll have time to carefully go through the pymc internals for that until later this week

OK, but given that nuts is working fine it's likely that the gradients are correct, no?

No worries, maybe I will find time to have a look, or we just wait. 👍

[janfb]

actually, I ran the CD workflow with slow tests and they are passing now (we got lucky?).
I will run it again to see how far we can push it.

[janfb]

Tests are still passing, and I checked the posterior visually as well - all seems fine!

Thanks for solving this @felixp8 ! 👏