Simplify mcmc module

[michaelosthege]

What is this PR about?

I'm refactoring mcmc.py (ex sampling.py) to prepare for extraction of population-sampling related code from mcmc.py.

Next to the simplification and moving of code, I also removed support for selecting which variables to include in the trace.
I have never seen this applied anywhere, but anybody feel free to object.
However, if we decide to not make this breaking change, we should still refactor the internal functions towards a clear distinction of trace vs. trace_vars.

Major / Breaking Changes

• Removed support for selectively tracking variables via pm.sample(trace=[...]).

Bugfixes / New features

• None

Docs / Maintenance

• Moved internal functions in mcmc.py down into other modules.

[codecov]

Codecov Report

Merging #6269 (21e9824) into main (781d974) will decrease coverage by 11.92%.
The diff coverage is 69.49%.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #6269       +/-   ##
===========================================
- Coverage   94.38%   82.46%   -11.93%     
===========================================
  Files         108      111        +3     
  Lines       23839    23820       -19     
===========================================
- Hits        22501    19643     -2858     
- Misses       1338     4177     +2839     

Impacted Files	Coverage Δ
pymc/tests/backends/test_base.py	0.00% <0.00%> (ø)
pymc/backends/base.py	68.09% <14.28%> (-19.57%)	⬇️
pymc/sampling/population.py	71.42% <71.42%> (ø)
pymc/stats/convergence.py	92.72% <91.66%> (-0.21%)	⬇️
pymc/sampling/mcmc.py	92.29% <100.00%> (+2.25%)	⬆️
pymc/tests/sampling/test_mcmc.py	98.61% <100.00%> (-0.14%)	⬇️
pymc/tests/sampling/test_population.py	100.00% <100.00%> (ø)
pymc/tests/stats/test_convergence.py	100.00% <100.00%> (ø)
pymc/tests/step_methods/test_metropolis.py	100.00% <100.00%> (ø)
pymc/tests/backends/test_ndarray.py	0.00% <0.00%> (-100.00%)	⬇️
... and 20 more

[ricardoV94]

Next to the simplification and moving of code, I also removed support for selecting which variables to include in the trace.

Is this similar to the "broken functionality" in this issue: #6116. If so we could also remove it there and close the issue

[michaelosthege]

Is this similar to the "broken functionality" in this issue: #6116. If so we could also remove it there and close the issue

This might be a matter of incorrect type annotation: In pm.sample the trace was advertised as List[str] (among other types), but the test case actually fed a List[TensorVariable]. I don't know if List[str] even worked.

But yes, it sounds like a similar feature.

If we want to support this, I would suggest to reintroduce it with a separate kwarg trace_vars: Optional[Sequence[str]] (str because we'll only want to support named RVs..).