Rename and refactor start dict in sampling

[michaelosthege]

This PR is in preparation of switching to the new initval framework.

To make debugging and reviewing a little easier, I added type hints and moved the start-related code closer together.

API/Behavior changes:

• A few lines related to the now unsupported use of length-zero traces as pm.sample inputs were removed.
• The result from init_nuts is now always used as the initial/starting point, whereas before it was only used unless a start dict was manually specified. init_nuts itself combines the automatically determined initial point with the user-provided initvals such that initvals take priority.
• The pm.sample(start=...) kwarg was renamed to initvals, to reflect that it takes the same keys/values/signature as model.initial_values or the corresponding Distribution.__new__(initval=...) kwarg.
• start kwargs of lower-level sampling functions are now required to be numeric & complete. model.update_start_vals is no longer applied by lower-level functions.
• Moving forward only pm.sample(initvals=...) and init_nuts(initvals=...) take the fully-flexibly initval-style dictionary of potentially incomplete (and soon also symbolic, "prior", or "moment" valued) initval strategies.
• Checks of non-inf/nan initial points and corresponding shapes now run under all circumstances.

[codecov]

Codecov Report

Merging #5027 (6156cbb) into main (641b278) will increase coverage by 0.01%.
The diff coverage is 83.33%.

❗ Current head 6156cbb differs from pull request most recent head 75f4c46. Consider uploading reports for the commit 75f4c46 to get more accurate results

@@            Coverage Diff             @@
##             main    #5027      +/-   ##
==========================================
+ Coverage   77.82%   77.83%   +0.01%     
==========================================
  Files         128      128              
  Lines       24380    24384       +4     
==========================================
+ Hits        18973    18980       +7     
+ Misses       5407     5404       -3     

Impacted Files	Coverage Δ
pymc/sampling.py	87.06% <81.81%> (+0.04%)	⬆️
pymc/parallel_sampling.py	87.33% <100.00%> (+1.04%)	⬆️

[michaelosthege]

@aseyboldt the only remaining test failure is limited to float32. The test was written by you 4 years ago and I can't tell why it failed:
https://github.com/pymc-devs/pymc3/pull/5027/checks?check_run_id=3720168022#step:7:2486

I was able to establish that the initial point that failes the _check_start_shape() was {'a': array([0., 0.], dtype=float32), 'c': array([0., 0.], dtype=float32)}.

[michaelosthege]

I XFAILed the test, since the error appears in a branch (start shape checking) that was not triggered before.

[ricardoV94]

Needs a release note

[michaelosthege]

I'm collecting all release notes in the Hackmd document. Also there will be another update on this API with the next PR.

If that's fine with you, I will update the release notes in the next PR?

[aloctavodia]

better to simply use "start" instead of renaming the variable.

[michaelosthege]

I decided against that because the "point" variable is overwritten all over again while iterating the draws. So it's no longer the "start" after the first iteration and I wanted to avoid confusion because of lines like strace.record(start, stats).

[michaelosthege]

Thanks @aloctavodia ! With the exception of one item I implemented your suggestions :)

Please let me know if we can move forward with this PR.

[michaelosthege]

I decided against that because the "point" variable is overwritten all over again while iterating the draws. So it's no longer the "start" after the first iteration and I wanted to avoid confusion because of lines like strace.record(start, stats).