Add test to compare draws when var_names is used in pm.sample()

tests/sampling/test_mcmc.py

@@ -695,12 +695,39 @@ def test_no_init_nuts_compound(caplog):
 
 
 def test_sample_var_names():
-    with pm.Model() as model:
-        a = pm.Normal("a")
-        b = pm.Deterministic("b", a**2)
-        idata = pm.sample(10, tune=10, var_names=["a"])
-        assert "a" in idata.posterior
-        assert "b" not in idata.posterior
+    # Generate data
+    seed = 1234
+    rng = np.random.default_rng(seed)
+
+    group = rng.choice(list("ABCD"), size=100)
+    x = rng.normal(size=100)
+    y = rng.normal(size=100)
+
+    group_values, group_idx = np.unique(group, return_inverse=True)
+
+    coords = {"group": group_values}
+
+    # Create model
+    with pm.Model(coords=coords) as model:
+        b_group = pm.Normal("b_group", dims="group")
+        b_x = pm.Normal("b_x")
+        mu = pm.Deterministic("mu", b_group[group_idx] + b_x * x)
+        sigma = pm.HalfNormal("sigma")
+        pm.Normal("y", mu=mu, sigma=sigma, observed=y)
+
+    # Sample with and without var_names, but always with the same seed
+    with model:
+        idata_1 = pm.sample(tune=100, draws=100, random_seed=seed)
+        idata_2 = pm.sample(
+            tune=100, draws=100, var_names=["b_group", "b_x", "sigma"], random_seed=seed
+        )
+
+    assert "mu" in idata_1.posterior
+    assert "mu" not in idata_2.posterior
+
+    assert np.all(idata_1.posterior["b_group"] == idata_2.posterior["b_group"]).item()
+    assert np.all(idata_1.posterior["b_x"] == idata_2.posterior["b_x"]).item()
+    assert np.all(idata_1.posterior["sigma"] == idata_2.posterior["sigma"]).item()
 
 
 class TestAssignStepMethods: