Refactor sample_posterior_predictive_w for V4

[zaxtax]

This tries to address #4807

Right now, it passes all unit tests, but doesn't use the fast sampling procedure of sample_posterior_predictive

The code is also not feature-complete.

[ricardoV94]

fast posterior_predictive_sampling no longer exists (everything is fast now). Also some tweaks will be needed following #5787 which should be merged soon!

[codecov]

Codecov Report

Merging #5800 (6683916) into main (1e7d91f) will increase coverage by 0.43%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #5800      +/-   ##
==========================================
+ Coverage   88.99%   89.43%   +0.43%     
==========================================
  Files          74       74              
  Lines       13809    13807       -2     
==========================================
+ Hits        12290    12348      +58     
+ Misses       1519     1459      -60     

Impacted Files	Coverage Δ
pymc/sampling.py	89.68% <100.00%> (+7.16%)	⬆️
pymc/parallel_sampling.py	86.46% <0.00%> (-1.00%)	⬇️
pymc/backends/base.py	86.44% <0.00%> (-0.74%)	⬇️

[zaxtax]

Let me make those tweaks and push tonight.

[ricardoV94]

This won't be conditioned on the posterior samples.

You will have to create a custom function similarly to what sample_posterior_predictive does. See recent changes in #5759

[ricardoV94]

It might also be useful to compare what changed between V3 and V4 in sample_posterior_predictive because some of the things in sample_posterior_predictive_w might no longer be needed / make sense

[zaxtax]

Closing in favour of #6254