Add rice tests

[MBrouns]

Continuation from #2963. I rebased to get rid of the merge commit and got the tests to pass by changing the tested domain to Rplusbig.

The problem with large values of value and nu is that the regular i0 function will overflow to inf. Scipy seems to go around this by slightly modifying the original function from:

x * exp(-(x**2+b**2)/2) * I[0](x*b) to: x * np.exp(-(x-b)*(x-b)/2.0) * sc.i0e(x*b)

The i0e function is then partitioned into two intervals: [0, 8] and (8, infinity) which are implemented slightly different:

  if (x <= 8.0) {
	y = (x / 2.0) - 2.0;
	return (chbevl(y, A, 30));
    }

    return (chbevl(32.0 / x - 2.0, B, 25) / sqrt(x));

If we want the Rice distribution to be able to handle larger values for value and nu we would need to implement a similar strategy but I am unsure on how exactly to implement this in PyMC3. Would this PR be acceptable without that?

[ColCarroll]

Sorry this sat for so long -- looks good to me, other than the one comment!

[ColCarroll]

these two are actually implemented in theano now: https://github.com/Theano/Theano/blob/master/theano/scalar/basic_scipy.py

[MBrouns]

Okay that was a great comment! I used the same implementation of i0 in theano to implement the i0e function which is used in scipy to improve the numerical stability of the pdf for large values of value and nu. That means the tests can use a much larger domain now for testing!

[ColCarroll]

Looks like there is merging trouble. My fork is named origin, and this main version is called upstream (check with git remote -v). If your setup is the same, you would run

git fetch upstream
git rebase upstream/master
git push -u origin +add_rice_tests

Notice the + on that last line, which breaks history on your version (so don't do that on master for a general project), but won't matter to us when we merge.

[MBrouns]

I can't seem to reproduce the failing test case on my local machine. I'm using python 2.7 and set the FLOATX env var to float32. Any idea what's happening?

[ColCarroll]

That looks strange - like the output is -inf when you expect it to be like, -109.

Replicating the tests is a little tough (you need to set $THEANO_FLAGS, not $FLOATX). I can try on my machine later, but I think this is the invocation if you have things set up in a python 2.7 environment:

THEANO_FLAGS='floatX=float32,gcc.cxxflags='\''-march=core2'\''' python -m pytest -xv pymc3/tests/test_distributions.py::TestMatchesScipy::test_rice

[MBrouns]

Tests are passing now!

[ColCarroll]

Looks good to me -- thanks for the contribution, @MBrouns!