Refactor Factor properties

[ricardoV94]

This PR deprecates most of the Factor properties, and gives the following default methods:

• compile_logp(self, vars=None, jacobian=True, sum=True):
• compile_dlogp(self, vars=None, jacobian=True):
• compile_d2logp(self, vars=None, jacobian=True):

The prefix compile is there to make it obvious this is a costly operation, and that the results should be cached once and reused afterwards. Also this makes it easier to deprecate the old properties, which couldn't easily be changed into methods.

It also deprecates LoosePointFunc and renames FastPointFunc to PointFunc which is now the default. This closes #5318.

Finally this PR also renames pm.logpt to pm.joint_logpt, which is now the main bridge between PyMC and Aeppl. The reason for this is that pm.logpt has diverged quite a lot from what it was doing in V3, and because of that it has a lot of ugly internal logic that should be handled by the Model object instead (involving trying to find value variables, transforms and scaling in the tags of the variables). The rename will hopefully help break the dependency that's there for backwards compat and facilitate refactoring in the future, such as #5033.

---

It would be nice to find a nice way to transition from Model.logpt being a property -> method that can accept vars, jacobian and sum as an argument. Then we can remove the more verbose logp_elemwiset, which is temporarily playing this more flexible role, in service of all other methods and properties Decided to break away immediately following discussion in #5333

[codecov]

Codecov Report

Merging #5320 (a1e30eb) into main (1b32070) will increase coverage by 0.11%.
The diff coverage is 91.39%.

❗ Current head a1e30eb differs from pull request most recent head 75ea232. Consider uploading reports for the commit 75ea232 to get more accurate results

@@            Coverage Diff             @@
##             main    #5320      +/-   ##
==========================================
+ Coverage   80.23%   80.34%   +0.11%     
==========================================
  Files          89       89              
  Lines       14856    14805      -51     
==========================================
- Hits        11919    11895      -24     
+ Misses       2937     2910      -27     

Impacted Files	Coverage Δ
pymc/backends/arviz.py	90.28% <ø> (ø)
pymc/distributions/__init__.py	100.00% <ø> (ø)
pymc/model_graph.py	85.51% <ø> (ø)
pymc/step_methods/sgmcmc.py	0.00% <0.00%> (ø)
pymc/tuning/starting.py	92.56% <83.33%> (+9.36%)	⬆️
pymc/step_methods/metropolis.py	83.05% <85.71%> (ø)
pymc/model.py	85.93% <92.64%> (+1.70%)	⬆️
pymc/backends/base.py	86.56% <100.00%> (ø)
pymc/distributions/logprob.py	96.36% <100.00%> (-0.13%)	⬇️
pymc/sampling.py	86.31% <100.00%> (-0.11%)	⬇️
... and 9 more

[michaelosthege]

Sorry about that nitpick, but given how much code calls these properties/methods, could you add some type hints?
Even incomplete type hints here can give a lot of mypy coverage, right?

[twiecki]

This is shaping up to be a really nice refactor of some quite obscure code.

[ricardoV94]

This is shaping up to be a really nice refactor of some quite obscure code.

Hopefully one will also be less lost when doing autocomplete on a Model to find a method xD

[michaelosthege]

I'm open to having docstring link to docstrings of the other properties/methods.
We can probably make the necessary changes all as suggestions and have one commit for them?

[ricardoV94]

I'm open to having docstring link to docstrings of the other properties/methods. We can probably make the necessary changes all as suggestions and have one commit for them?

Yeah I think the compile_* is better of just directing to the respective methods for the meaning of the variables. Feel free to make changes and force-push to this branch! Won't have time to work on this until next week