diff --git a/pymc/aesaraf.py b/pymc/aesaraf.py
index 0fdb53acfd..bcb1bfa00b 100644
--- a/pymc/aesaraf.py
+++ b/pymc/aesaraf.py
@@ -444,6 +444,9 @@ def intX(X):
     """
     Convert a aesara tensor or numpy array to aesara.tensor.int32 type.
     """
+    # check value is already int, do nothing in this case
+    if (hasattr(X, "dtype") and "int" in str(X.dtype)) or isinstance(X, int):
+        return X
     intX = _conversion_map[aesara.config.floatX]
     try:
         return X.astype(intX)
diff --git a/pymc/distributions/discrete.py b/pymc/distributions/discrete.py
index fc57448584..a6db6b70c8 100644
--- a/pymc/distributions/discrete.py
+++ b/pymc/distributions/discrete.py
@@ -878,7 +878,11 @@ def dist(cls, N, k, n, *args, **kwargs):
         return super().dist([good, bad, n], *args, **kwargs)
 
     def moment(rv, size, good, bad, n):
-        N, k = good + bad, good
+        # Cast to float because the intX can be int8
+        # which could trigger an integer overflow below.
+        n = floatX(n)
+        k = floatX(good)
+        N = k + floatX(bad)
         mode = at.floor((n + 1) * (k + 1) / (N + 2))
         if not rv_size_is_none(size):
             mode = at.full(size, mode)
@@ -1014,6 +1018,8 @@ def dist(cls, lower, upper, *args, **kwargs):
         return super().dist([lower, upper], **kwargs)
 
     def moment(rv, size, lower, upper):
+        upper = floatX(upper)
+        lower = floatX(lower)
         mode = at.maximum(at.floor((upper + lower) / 2.0), lower)
         if not rv_size_is_none(size):
             mode = at.full(size, mode)
diff --git a/pymc/tests/distributions/util.py b/pymc/tests/distributions/util.py
index 0a501da4e8..a6adba6097 100644
--- a/pymc/tests/distributions/util.py
+++ b/pymc/tests/distributions/util.py
@@ -579,7 +579,7 @@ def assert_moment_is_expected(model, expected, check_finite_logp=True):
 
     assert moment.shape == expected.shape
     assert expected.shape == random_draw.shape
-    assert np.allclose(moment, expected)
+    np.testing.assert_allclose(moment, expected, atol=1e-10)
 
     if check_finite_logp:
         logp_moment = (
diff --git a/pymc/tests/test_aesaraf.py b/pymc/tests/test_aesaraf.py
index f627d932fa..05a9137397 100644
--- a/pymc/tests/test_aesaraf.py
+++ b/pymc/tests/test_aesaraf.py
@@ -244,7 +244,7 @@ def test_convert_observed_data(input_dtype):
     assert isinstance(aesara_output, Variable)
     npt.assert_allclose(aesara_output.eval(), aesara_graph_input.eval())
     intX = pm.aesaraf._conversion_map[aesara.config.floatX]
-    if dense_input.dtype == intX or dense_input.dtype == aesara.config.floatX:
+    if "int" in str(dense_input.dtype) or dense_input.dtype == aesara.config.floatX:
         assert aesara_output.owner is None  # func should not have added new nodes
         assert aesara_output.name == input_name
     else:
@@ -254,7 +254,8 @@ def test_convert_observed_data(input_dtype):
     if "float" in input_dtype:
         assert aesara_output.dtype == aesara.config.floatX
     else:
-        assert aesara_output.dtype == intX
+        # only cast floats, leave ints as is
+        assert aesara_output.dtype == input_dtype
 
     # Check function behavior with generator data
     generator_output = func(square_generator)
diff --git a/pymc/tests/test_data.py b/pymc/tests/test_data.py
index 52b18705ba..4536786e88 100644
--- a/pymc/tests/test_data.py
+++ b/pymc/tests/test_data.py
@@ -87,7 +87,7 @@ def test_sample_posterior_predictive_after_set_data(self):
             )
         # Predict on new data.
         with model:
-            x_test = [5, 6, 9]
+            x_test = [5.0, 6.0, 9.0]
             pm.set_data(new_data={"x": x_test})
             y_test = pm.sample_posterior_predictive(trace)
 
@@ -111,7 +111,7 @@ def test_sample_posterior_predictive_after_set_data_with_coords(self):
             )
         # Predict on new data.
         with model:
-            x_test = [5, 6]
+            x_test = [5.0, 6.0]
             pm.set_data(new_data={"x": x_test}, coords={"obs_id": ["a", "b"]})
             pm.sample_posterior_predictive(idata, extend_inferencedata=True, predictions=True)