TST: adjust ess test for new accept rate in 2.15

In 2.15, @betanalpha "changed the way the accept rate was calculated by
excluding the initial state from the numerator and denominator."[^1]
This lowers the ess considerably for the simple model used in this test.

[^1] http://discourse.mc-stan.org/t/much-lower-effective-sample-size-with-2-15/348

Author: ariddell

pystan/tests/test_ess.py

@@ -4,19 +4,20 @@
 import pystan.chains
 import pystan._chains
 
-# NOTE: This test is fragile because there is no guarantee that samples are
-# consistent between Stan releases (even with fixed random seeds).  Consider
-# this a smoke test.
+# NOTE: This test is fragile because the default sampling algorithm used by Stan
+# may change in significant ways.
+
 
 class TestESS(unittest.TestCase):
 
     @classmethod
     def setUpClass(cls):
         model_code = 'parameters {real y;} model {y ~ normal(0,1);}'
-        model = pystan.StanModel(model_code=model_code, model_name="normal2")
-        cls.fit = model.sampling(iter=4000, chains=2, seed=5)
+        model = pystan.StanModel(model_code=model_code)
+        cls.fits = [model.sampling(iter=4000, chains=2, seed=i) for i in range(10)]
 
     def test_ess(self):
-        sim = self.fit.sim
-        ess = pystan.chains.ess(sim, sim['fnames_oi'].index('y'))
-        self.assertGreater(ess, 2000)
+        sims = [fit.sim for fit in self.fits]
+        esses = [pystan.chains.ess(sim, sim['fnames_oi'].index('y')) for sim in sims]
+        # in Stan 2.15 the default acceptance rate was changed, ess dropped
+        self.assertGreater(sum(esses) / len(esses), 1200)