Change initial_point default strategy from "prior" to "moment"

[ricardoV94]

This PR adds a check that we have moments for all distributions and changes the default initial point strategy from "prior" to "moment"

Also added a check in the default test moments that the logp of the provided moment is finite.

Closes #5009
Related to #5078

We also need to decide whether we default to a draw from the prior if a distribution does not have a get_moment implemented or if we just fail in that case (which is what is happening now). It would be trivial to allow this with a try/except block

[codecov]

Codecov Report

Merging #5140 (c6e11eb) into main (0c90e82) will increase coverage by 0.01%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #5140      +/-   ##
==========================================
+ Coverage   79.15%   79.17%   +0.01%     
==========================================
  Files          88       88              
  Lines       14311    14316       +5     
==========================================
+ Hits        11328    11334       +6     
+ Misses       2983     2982       -1     

Impacted Files	Coverage Δ
pymc/distributions/continuous.py	97.37% <ø> (+0.50%)	⬆️
pymc/initial_point.py	100.00% <100.00%> (ø)
pymc/backends/report.py	89.51% <0.00%> (-2.10%)	⬇️
pymc/parallel_sampling.py	86.33% <0.00%> (-1.00%)	⬇️
pymc/distributions/discrete.py	98.72% <0.00%> (+0.25%)	⬆️
pymc/distributions/distribution.py	95.23% <0.00%> (+0.52%)	⬆️

[ricardoV94]

Getting some weird parallel sampling test failures only on Windows. Perhaps related to #4904?

[ricardoV94]

I am inclined to defaulting back to a prior sample if a distribution does not have a moment, perhaps with a UserWarning like

Moment not defined for distribution X, defaulting to a draw from the prior. This can lead to difficulties during tuning. You can manually define an initval or implement a get_moment dispatched function for this distribution.

This would allow users to more gradually implement their own distributions. We still have a check added in this PR that all our standard distributions have moments implemented.

[michaelosthege]

I like the fallback plus warning idea. Maybe include a link to the relevant docs section on implementing custom distributions?

[ricardoV94]

We have very few moments missing, and it was consensus that this should no longer block the beta release.

I have added the known missing moments to test_all_distributions_have_moments. This test will fail whenever those moments get implemented, making sure our coverage stays up to date.

[ricardoV94]

Still have those surprising failing tests on Windows alone...

[michaelosthege]

Still have those surprising failing tests on Windows alone...

To me it looks like the same problem as #4904 - broadcasts are not correctly propagated through Cast operations.

[ricardoV94]

Windows issues are related to a mix of:

1. RandomVariables have unnecessary SpecifyShape when size is casted aesara-devs/aesara#691,
2. Wrong broadcastable output of Alloc when using SpecifyShape aesara-devs/aesara#692

[ricardoV94]

Tests are passing with the latest Aesara version