Refactor DensityDist into v4

[lucianopaz]

Closes #4831

This PR ports DensityDist into v4. It creates a DensityDistRV class and DensityDist class in a similar way as is done by the Simulator class. When a DensityDist is created, it registers the logp, logcdf and get_moment functions for the associated Op type. The DensityDistRV is used to overload the rng_fn from the base class to be able to run the user supplied random callable with the appropriate signature.

Depending on what your PR does, here are a few things you might want to address in the description:

• what are the (breaking) changes that this PR makes?

The signature of DensityDist is completely different than in v3:

• It now takes as positional arguments, the distribution parameters. In v3, these were passed in through a dictionary that was supplied as observed. The associated MultiObservedRV is no longer used or needed and can be removed in a following PR.
• logp is now an optional keyword only argument instead of the first positional argument. If users try to pass it as the first positional argument, they will get an exception that tells them that they are using the old v3 API and should change.
• The signature of logp is now different, it takes in the distribution parameters as positional arguments. Something similar happens for random.
• All the distribution methods: logp, random, logcdf and get_moment are optional. If they are not passed during construction, the RV will be built, but a NotImplementedError will be raised when you try to do something like pm.sample, pm.sample_prior_predictive or get_moment.

• important background, or details about the implementation
• are the changes—especially new features—covered by tests and docstrings?

The docstrings were updated and new tests have been added for the different optional methods (except logcdf) which behaves in the same way as logp. If necessary, it's possible to add tests for logcdf too.

• linting/style checks have been run
• consider adding/updating relevant example notebooks
• right before it's ready to merge, mention the PR in the RELEASE-NOTES.md

[codecov]

Codecov Report

Merging #5026 (b9b9ea1) into main (37ba9a3) will increase coverage by 0.45%.
The diff coverage is 96.06%.

@@            Coverage Diff             @@
##             main    #5026      +/-   ##
==========================================
+ Coverage   77.85%   78.31%   +0.45%     
==========================================
  Files         128      129       +1     
  Lines       24349    24400      +51     
==========================================
+ Hits        18958    19108     +150     
+ Misses       5391     5292      -99     

Impacted Files	Coverage Δ
pymc/tests/test_model.py	99.11% <ø> (+0.88%)	⬆️
pymc/gp/gp.py	60.25% <50.00%> (+15.33%)	⬆️
pymc/distributions/distribution.py	94.62% <92.15%> (+7.46%)	⬆️
pymc/tests/test_distributions.py	96.34% <100.00%> (+0.33%)	⬆️
pymc/tests/test_distributions_random.py	86.28% <100.00%> (+1.63%)	⬆️
pymc/tests/test_gp.py	86.20% <100.00%> (+1.28%)	⬆️
pymc/tests/test_idata_conversion.py	96.20% <100.00%> (+2.72%)	⬆️
pymc/tests/test_moment.py	100.00% <100.00%> (ø)
pymc/tests/test_parallel_sampling.py	80.64% <100.00%> (+1.65%)	⬆️
pymc/tests/test_sampling.py	97.29% <100.00%> (+0.23%)	⬆️
... and 19 more

[michaelosthege]

The new initval framework will no longer fall back to the test_value. Furthermore this assignment doesn't have a lot of dimensionality flexibility, for example with symbolic size.

My recommendation is to take out the assignment and also the hack below.

[lucianopaz]

Yes, but the new initial value framework has not been finished, so I’ve used the same hack that Flat and HalfFlat use to get their initial values. I don’t think that this PR should have to wait for the new initial values framework to merge it.
In any case, over the new framework is in place, we could change the default initialisation used by density dist.

[michaelosthege]

I like it 👍

[twiecki]

Thanks @lucianopaz!