diana-hep / pyhf / 1549
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kratsg 
Use distributions in ML backends for better Poisson approximation (#268)

* Use TensorFlow Probability for distributions

The only real change is swapping out tf.distributions for
tfp.distributions, however this is a large improvement on the backend.

In addition, tfp is able to better approximate the continous
approximation to the Poisson distribution's p.m.f. while still providing
smooth gradients.

Also add some docstrings.

* Don't use the Normal approximation for the NumPy backend in testing

With improvments to the ML backends it isn't needed

* Use torch.distributions.Poisson for poisson p.m.f. approximation

Provides better approximation then the Normal approximation

* Use PyTorch's Poisson log_prob approximation for MXNet's poisson

This is just implimenting the code that exists at the moment in
PyTorch's library

* Add docstrings to NumPy backend poisson and normal

* Move examples to before Args and Returns

For style consistency in the docs

* Remove use of poisson_from_normal=True from everywhere

It is no longer needed for comparisons and so is not needed anywhere

Though as a result of this, loosen the tolerance for the standard
deviation of results in test_tensor to 5e-5

* Wrap json.load in with clause to safely load and close

Resolves issue of ResourceWarning: unclosed file <_io.TextIOWrapper
name='<your path here>/pyhf/pyhf/data/spec.json' mode='r' encoding='UTF-8'>

Additionally apply autopep8

* Wrap click.open_file in with clause to safely load and close

Resolves issue of ResourceWarning: unclosed file

* Split pytest into two runs given Travis memory constraints

If pytest runs all tests at once then it exceeds the alloted memory for
it by Travis CI. To deal with this, tests/test_notebooks is run by itself
in a second run of pytest. This is a bit strange, but seems to work.

As a result of this and the order that pyest runs the tests, the
docstring tests finish just befor... (continued)

1239 of 1259 relevant lines covered (98.41%)

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Jobs
ID Job ID Ran Files Coverage
1 1549.1 0
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2 1549.2 0
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3 1549.3 0
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4 1549.4 0
49.17
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5 1549.5 0
59.73
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6 1549.6 0
Travis Job 1549.6
Source Files on build 1549
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