NegativeBinomial distribution sample generator wrapper (#3866)

* Added wrapper for gamma sampling in negative binomial distribution.

* Fixed typo in posterior sampling warnings.

* Drop nuts init method from pm.sample (#3863)

* Dropped nuts init method

* Dropped nuts init method from tests

* Refined doc string and added release note

* Added wrapper for gamma sampling in negative binomial distribution.

* Fixed typo in posterior sampling warnings.

* Added test for negative binomial input shape.

* Updating release notes with changes to negative binomial sampling.
Co-authored-by: Alexandre ANDORRA <andorra.alexandre@gmail.com>

RELEASE-NOTES.md

@@ -19,6 +19,7 @@
 - In named models, `pm.Data` objects now get model-relative names (see [#3843](https://github.com/pymc-devs/pymc3/pull/3843)).
 - `pm.sample` now takes 1000 draws and 1000 tuning samples by default, instead of 500 previously (see [#3855](https://github.com/pymc-devs/pymc3/pull/3855)).
 - Dropped the outdated 'nuts' initialization method for `pm.sample` (see [#3863](https://github.com/pymc-devs/pymc3/pull/3863)).
+- Moved argument division out of `NegativeBinomial` `random` method. Fixes [#3864](https://github.com/pymc-devs/pymc3/issues/3864) in the style of [#3509](https://github.com/pymc-devs/pymc3/pull/3509).
 
 ## PyMC3 3.8 (November 29 2019)
 

pymc3/distributions/discrete.py

@@ -673,12 +673,24 @@ class NegativeBinomial(Discrete):
         array
         """
         mu, alpha = draw_values([self.mu, self.alpha], point=point, size=size)
-        g = generate_samples(stats.gamma.rvs, alpha, scale=mu / alpha,
+        g = generate_samples(self._random, mu=mu, alpha=alpha,
                              dist_shape=self.shape,
                              size=size)
         g[g == 0] = np.finfo(float).eps  # Just in case
         return np.asarray(stats.poisson.rvs(g)).reshape(g.shape)
 
+    def _random(self, mu, alpha, size):
+        """ Wrapper around stats.gamma.rvs that converts NegativeBinomial's
+        parametrization to scipy.gamma. All parameter arrays should have
+        been broadcasted properly by generate_samples at this point and size is
+        the scipy.rvs representation.
+        """
+        return stats.gamma.rvs(
+            a=alpha,
+            scale=mu / alpha,
+            size=size,
+        )
+
     def logp(self, value):
         """
         Calculate log-probability of NegativeBinomial distribution at specified value.

pymc3/sampling.py

@@ -1567,9 +1567,9 @@ def sample_posterior_predictive(
         nchain = 1
 
     if keep_size and samples is not None:
-        raise IncorrectArgumentsError("Should not specify both keep_size and samples argukments")
+        raise IncorrectArgumentsError("Should not specify both keep_size and samples arguments")
     if keep_size and size is not None:
-        raise IncorrectArgumentsError("Should not specify both keep_size and size argukments")
+        raise IncorrectArgumentsError("Should not specify both keep_size and size arguments")
 
     if samples is None:
         if isinstance(trace, MultiTrace):

pymc3/tests/test_distributions_random.py

@@ -1176,6 +1176,31 @@ class TestNestedRandom(SeededTest):
         with model:
             return pm.sample_prior_predictive(prior_samples)
 
+    @pytest.mark.parametrize(
+        ["prior_samples", "shape", "mu", "alpha"],
+        [
+            [10, (3,), (None, tuple()), (None, (3,))],
+            [10, (3,), (None, (3,)), (None, tuple())],
+            [10, (4, 3,), (None, (3,)), (None, (3,))],
+            [10, (4, 3,), (None, (3,)), (None, (4, 3))],
+        ],
+        ids=str,
+    )
+    def test_NegativeBinomial(
+        self,
+        prior_samples,
+        shape,
+        mu,
+        alpha,
+    ):
+        prior = self.sample_prior(
+            distribution=pm.NegativeBinomial,
+            shape=shape,
+            nested_rvs_info=dict(mu=mu, alpha=alpha),
+            prior_samples=prior_samples,
+        )
+        assert prior["target"].shape == (prior_samples,) + shape
+
     @pytest.mark.parametrize(
         ["prior_samples", "shape", "psi", "mu", "alpha"],
         [