Update expected behavior of sample in relation to global seeding.

Together, `test_sample_does_not_set_seed` and `test_parallel_sample_does_not_reuse_seed` covered two unspoken behaviors of `sample`:
1. When no seed is specified, PyMC shall not set global seed state of numpy in the main process.
2. When no seed is specified, sampling will depend on numpy global seeding state for reproducible behavior.

Point 1 is due to PyMC legacy dependency on global seeding for step samplers. It tries to minimize "damage" by only setting global seeds when it absolutely needs to, in order to ensure deterministic sampling. Ideally calls to `numpy.seed` would never be made.

Point 2 goes against NumPy current best practices of using None when defining new Generators / SeedSequences (https://numpy.org/doc/stable/reference/random/bit_generators/generated/numpy.random.SeedSequence.html#numpy.random.SeedSequence)

The refactored tests cover point 1 more directly, and assert the opposite of point 2.

RELEASE-NOTES.md

@@ -25,6 +25,7 @@ Also check out the [milestones](https://github.com/pymc-devs/pymc/milestones) fo
 
 All of the above apply to:
 
+⚠ Sampling functions no longer respect user-specified global seeding! Always pass `random_seed` to ensure reproducible behavior (see [#5787](https://github.com/pymc-devs/pymc/pull/5787)),
 Signature and default parameters changed for several distributions:
     - `pm.StudentT` now requires either `sigma` or `lam` as kwarg (see [#5628](https://github.com/pymc-devs/pymc/pull/5628))
     - `pm.StudentT` now requires `nu` to be specified (no longer defaults to 1) (see [#5628](https://github.com/pymc-devs/pymc/pull/5628))

pymc/tests/test_sampling.py

@@ -15,7 +15,6 @@
 import unittest.mock as mock
 
 from contextlib import ExitStack as does_not_raise
-from itertools import combinations
 from typing import Tuple
 
 import aesara
@@ -108,35 +107,44 @@ def test_random_seed(self, chains, seeds, cores, init):
         else:
             assert allequal
 
-    def test_sample_does_not_set_seed(self):
-        # This tests that when random_seed is None, the global seed is not affected
-        random_numbers = []
-        for _ in range(2):
+    @mock.patch("numpy.random.seed")
+    def test_default_sample_does_not_set_global_seed(self, mocked_seed):
+        # Test that when random_seed is None, `np.random.seed` is not called in the main
+        # process. Ideally it would never be called, but PyMC step samplers still rely
+        # on global seeding for reproducible behavior.
+        kwargs = dict(tune=2, draws=2, random_seed=None)
+        with self.model:
+            pm.sample(chains=1, **kwargs)
+            pm.sample(chains=2, cores=1, **kwargs)
+            pm.sample(chains=2, cores=2, **kwargs)
+        mocked_seed.assert_not_called()
+
+    def test_sample_does_not_rely_on_external_global_seeding(self):
+        # Tests that sampling does not depend on exertenal global seeding
+        kwargs = dict(
+            tune=2,
+            draws=20,
+            random_seed=None,
+            return_inferencedata=False,
+        )
+        with self.model:
+            np.random.seed(1)
+            idata11 = pm.sample(chains=1, **kwargs)
+            np.random.seed(1)
+            idata12 = pm.sample(chains=2, cores=1, **kwargs)
             np.random.seed(1)
-            with self.model:
-                pm.sample(1, tune=0, chains=1, random_seed=None)
-                random_numbers.append(np.random.random())
-        assert random_numbers[0] == random_numbers[1]
-
-    def test_parallel_sample_does_not_reuse_seed(self):
-        cores = 4
-        random_numbers = []
-        draws = []
-        for _ in range(2):
-            np.random.seed(1)  # seeds in other processes don't effect main process
-            with self.model:
-                idata = pm.sample(100, tune=0, cores=cores)
-            # numpy thread mentioned race condition.  might as well check none are equal
-            for first, second in combinations(range(cores), 2):
-                first_chain = idata.posterior["x"].sel(chain=first).values
-                second_chain = idata.posterior["x"].sel(chain=second).values
-                assert not np.allclose(first_chain, second_chain)
-            draws.append(idata.posterior["x"].values)
-            random_numbers.append(np.random.random())
-
-        # Make sure future random processes aren't effected by this
-        assert random_numbers[0] == random_numbers[1]
-        assert (draws[0] == draws[1]).all()
+            idata13 = pm.sample(chains=2, cores=2, **kwargs)
+
+            np.random.seed(1)
+            idata21 = pm.sample(chains=1, **kwargs)
+            np.random.seed(1)
+            idata22 = pm.sample(chains=2, cores=1, **kwargs)
+            np.random.seed(1)
+            idata23 = pm.sample(chains=2, cores=2, **kwargs)
+
+        assert np.all(idata11["x"] != idata21["x"])
+        assert np.all(idata12["x"] != idata22["x"])
+        assert np.all(idata13["x"] != idata23["x"])
 
     def test_sample(self):
         test_cores = [1]