feat: Allow zero rate Poisson

[matthewfeickert]

Description

• Resolves Should Poisson[0,0] be handled especially? #293
• Closes Motivation for allowing zero rate in Poisson in v0.11.0? tensorflow/probability#1025

Allow zero rate Poisson under the case that the limit \lambda -> 0 is well defined as

    P(n | \lambda = 0) = { 1 if n = 0
                         { 0 otherwise

This PR enforces the default behavior across all backends.

This PR effectively reverts most of PR #1001 and PR #280, and reapplies most of @wiso's PR #277.

To allow for zero rate Poisson across all backends, the mimimum required versions are adjusted:

• Zero rate Poisson support was added to TensorFlow Probability in release v0.11.0, which requires tensorflow>=2.3 (c.f. Motivation for allowing zero rate in Poisson in v0.11.0? tensorflow/probability#1025). As a result, the minimum compatible releases are bumped to TensorFlow v2.3.1 and TensorFlow Probability v0.11.0.
• Zero rate Poisson support was added to PyTorch in release v1.10.0, so the minimum compatible release is set to that.
• This is already supported in SciPy stats, though @andrewfowlie asked that this be clarified in the docs in scipy.stats.poisson docs for rate = 0 scipy/scipy#12113

Note, that Issue #293 introduces the idea of a cutoff. That isn't off the table, but should be discussed in a separate Issue.

(Self note: As it will probably come up again at some point, the first citation of this being a thing that I can find is from this Cross Validated post.)

Checklist Before Requesting Reviewer

• Tests are passing
• "WIP" removed from the title of the pull request
• Selected an Assignee for the PR to be responsible for the log summary

Before Merging

For the PR Assignees:

• Summarize commit messages into a comprehensive review of the PR

* Effectively reverts most of PR #1001 and PR #280, reapplies most
of PR #277
* Use scipy.special.xlogy in Poisson computation for numpy backend
and use jax.scipy.special.xlogy for jax backend
* Set minimum required PyTorch to v1.10 for API stability
   - c.f. https://github.com/pytorch/pytorch/pull/61511 in torch v1.10.0
* Set minimum required TensorFlow to v2.3.1 and TensorFlow Probability
to v0.11.0
   - tfp v0.11.0 supports zero rate Poisson and requires tensorflow>=2.3.0
* Add note to docs that limit Poisson(n = 0 | lambda -> 0) = 1 is being used
* Update tests to use limit Poisson(n = 0 | lambda -> 0) = 1 result
* Run doctest on only the latest Python release

Co-authored-by: Ruggero Turra <[email protected]>

[matthewfeickert]

Relevant RTD build page: https://pyhf--1657.org.readthedocs.build/en/1657/_generated/pyhf.tensor.numpy_backend.numpy_backend.html#pyhf.tensor.numpy_backend.numpy_backend.poisson

[matthewfeickert]

cc @wiso, @alexander-held, @andrewfowlie as you've all participated in discussion on Issue #293.

[codecov]

Codecov Report

Merging #1657 (652813a) into master (8a3dc6b) will decrease coverage by 0.00%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1657      +/-   ##
==========================================
- Coverage   98.04%   98.04%   -0.01%     
==========================================
  Files          63       63              
  Lines        4145     4142       -3     
  Branches      572      572              
==========================================
- Hits         4064     4061       -3     
  Misses         48       48              
  Partials       33       33              

Flag	Coverage Δ
contrib	24.89% <25.00%> (-0.01%)	⬇️
doctest	60.98% <100.00%> (-0.03%)	⬇️
unittests	96.33% <100.00%> (-0.01%)	⬇️

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Impacted Files	Coverage Δ
src/pyhf/tensor/pytorch_backend.py	98.41% <ø> (ø)
src/pyhf/tensor/jax_backend.py	97.08% <100.00%> (ø)
src/pyhf/tensor/numpy_backend.py	98.47% <100.00%> (ø)
src/pyhf/tensor/tensorflow_backend.py	97.22% <100.00%> (-0.06%)	⬇️

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