Restrict domain on alpha in the CAR distribution

pymc/distributions/multivariate.py

@@ -2061,6 +2061,7 @@ def make_node(self, rng, size, dtype, mu, W, alpha, tau):
             W = Assert(msg)(W, pt.allclose(W, W.T))
 
         tau = pt.as_tensor_variable(floatX(tau))
+
         alpha = pt.as_tensor_variable(floatX(alpha))
 
         return super().make_node(rng, size, dtype, mu, W, alpha, tau)
@@ -2077,6 +2078,9 @@ def rng_fn(cls, rng: np.random.RandomState, mu, W, alpha, tau, size):
         Journal of the Royal Statistical Society Series B, Royal Statistical Society,
         vol. 63(2), pages 325-338. DOI: 10.1111/1467-9868.00288
         """
+        if np.all(alpha >= 1) or np.all(alpha <= -1):
+            raise ValueError("the domain of alpha is: -1 < alpha < 1")
+
         if not scipy.sparse.issparse(W):
             W = scipy.sparse.csr_matrix(W)
         s = np.asarray(W.sum(axis=0))[0]
@@ -2143,8 +2147,9 @@ class CAR(Continuous):
         :func:`~pytensor.sparse.basic.as_sparse_or_tensor_variable` is
         used for this sparse or tensorvariable conversion.
     alpha : tensor_like of float
-        Autoregression parameter taking values between -1 and 1. Values closer to 0 indicate weaker
-        correlation and values closer to 1 indicate higher autocorrelation. For most use cases, the
+        Autoregression parameter taking values greater than -1 and less than 1.
+        Values closer to 0 indicate weaker correlation and values closer to
+        1 indicate higher autocorrelation. For most use cases, the
         support of alpha should be restricted to (0, 1).
     tau : tensor_like of float
         Positive precision variable controlling the scale of the underlying normal variates.
@@ -2211,10 +2216,10 @@ def logp(value, mu, W, alpha, tau):
         logquad = (tau * delta * tau_dot_delta).sum(axis=-1)
         return check_parameters(
             0.5 * (logtau + logdet - logquad),
-            -1 <= alpha,
-            alpha <= 1,
+            -1 < alpha,
+            alpha < 1,
             tau > 0,
-            msg="-1 <= alpha <= 1, tau > 0",
+            msg="-1 < alpha < 1, tau > 0",
         )
 
 

tests/distributions/test_multivariate.py

@@ -835,6 +835,23 @@ def test_car_matrix_check(sparse):
             car_dist = pm.CAR.dist(mu, W, alpha, tau)
 
 
+@pytest.mark.parametrize("alpha", [1, -1])
+def test_car_alpha(alpha):
+    """
+    Tests the check that -1 < alpha < 1
+    """
+
+    W = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])
+
+    tau = 1
+    mu = np.array([0, 0, 0])
+
+    car_dist = pm.CAR.dist(W=W, alpha=alpha, mu=mu, tau=tau)
+
+    with pytest.raises(ValueError, match="the domain of alpha is: -1 < alpha < 1"):
+        pm.draw(car_dist)
+
+
 class TestLKJCholeskCov:
     def test_dist(self):
         sd_dist = pm.Exponential.dist(1, size=(10, 3))