diff --git a/pymc/stats/log_density.py b/pymc/stats/log_density.py
index a26f8aa60df..3216e26f3ee 100644
--- a/pymc/stats/log_density.py
+++ b/pymc/stats/log_density.py
@@ -12,7 +12,7 @@
 #   See the License for the specific language governing permissions and
 #   limitations under the License.
 from collections.abc import Sequence
-from typing import Literal
+from typing import Any, Literal
 
 from arviz import InferenceData
 from xarray import Dataset
@@ -36,6 +36,7 @@ def compute_log_likelihood(
     model: Model | None = None,
     sample_dims: Sequence[str] = ("chain", "draw"),
     progressbar=True,
+    compile_kwargs: dict[str, Any] | None = None,
 ):
     """Compute elemwise log_likelihood of model given InferenceData with posterior group
 
@@ -51,6 +52,8 @@ def compute_log_likelihood(
     model : Model, optional
     sample_dims : sequence of str, default ("chain", "draw")
     progressbar : bool, default True
+    compile_kwargs : dict[str, Any] | None
+        Extra compilation arguments to supply to :py:func:`~pymc.stats.compute_log_density`
 
     Returns
     -------
@@ -65,6 +68,7 @@ def compute_log_likelihood(
         kind="likelihood",
         sample_dims=sample_dims,
         progressbar=progressbar,
+        compile_kwargs=compile_kwargs,
     )
 
 
@@ -75,6 +79,7 @@ def compute_log_prior(
     model: Model | None = None,
     sample_dims: Sequence[str] = ("chain", "draw"),
     progressbar=True,
+    compile_kwargs=None,
 ):
     """Compute elemwise log_prior of model given InferenceData with posterior group
 
@@ -90,6 +95,8 @@ def compute_log_prior(
     model : Model, optional
     sample_dims : sequence of str, default ("chain", "draw")
     progressbar : bool, default True
+    compile_kwargs : dict[str, Any] | None
+        Extra compilation arguments to supply to :py:func:`~pymc.stats.compute_log_density`
 
     Returns
     -------
@@ -104,6 +111,7 @@ def compute_log_prior(
         kind="prior",
         sample_dims=sample_dims,
         progressbar=progressbar,
+        compile_kwargs=compile_kwargs,
     )
 
 
@@ -116,14 +124,42 @@ def compute_log_density(
     kind: Literal["likelihood", "prior"] = "likelihood",
     sample_dims: Sequence[str] = ("chain", "draw"),
     progressbar=True,
+    compile_kwargs=None,
 ) -> InferenceData | Dataset:
     """
     Compute elemwise log_likelihood or log_prior of model given InferenceData with posterior group
+
+    Parameters
+    ----------
+    idata : InferenceData
+        InferenceData with posterior group
+    var_names : sequence of str, optional
+        List of Observed variable names for which to compute log_prior.
+        Defaults to all all free variables.
+    extend_inferencedata : bool, default True
+        Whether to extend the original InferenceData or return a new one
+    model : Model, optional
+    kind: Literal["likelihood", "prior"]
+        Whether to compute the log density of the observed random variables (likelihood)
+        or to compute the log density of the latent random variables (prior). This
+        parameter determines the group that gets added to the returned `~arviz.InferenceData` object.
+    sample_dims : sequence of str, default ("chain", "draw")
+    progressbar : bool, default True
+    compile_kwargs : dict[str, Any] | None
+        Extra compilation arguments to supply to :py:func:`pymc.model.core.Model.compile_fn`
+
+    Returns
+    -------
+    idata : InferenceData
+        InferenceData with the ``log_likelihood`` group when ``kind == "likelihood"``
+        or the ``log_prior`` group when ``kind == "prior"``.
     """
 
     posterior = idata["posterior"]
 
     model = modelcontext(model)
+    if compile_kwargs is None:
+        compile_kwargs = {}
 
     if kind not in ("likelihood", "prior"):
         raise ValueError("kind must be either 'likelihood' or 'prior'")
@@ -150,6 +186,7 @@ def compute_log_density(
         inputs=umodel.value_vars,
         outs=umodel.logp(vars=vars, sum=False),
         on_unused_input="ignore",
+        **compile_kwargs,
     )
 
     coords, dims = coords_and_dims_for_inferencedata(umodel)
diff --git a/tests/stats/test_log_density.py b/tests/stats/test_log_density.py
index 0a8a79e0734..c7b120af257 100644
--- a/tests/stats/test_log_density.py
+++ b/tests/stats/test_log_density.py
@@ -11,6 +11,8 @@
 #   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 #   See the License for the specific language governing permissions and
 #   limitations under the License.
+from unittest.mock import patch
+
 import numpy as np
 import pytest
 import scipy.stats as st
@@ -174,3 +176,17 @@ def test_deterministic_log_prior(self):
             res.log_prior["x"].values,
             st.norm(0, 1).logpdf(idata.posterior["x"].values),
         )
+
+    def test_compilation_kwargs(self):
+        with Model() as m:
+            x = Normal("x")
+            Deterministic("d", 2 * x)
+            Normal("y", x, observed=[0, 1, 2])
+
+            idata = InferenceData(posterior=dict_to_dataset({"x": np.arange(100).reshape(4, 25)}))
+            with patch("pymc.model.core.compile_pymc") as patched_compile_pymc:
+                compute_log_prior(idata, compile_kwargs={"mode": "JAX"})
+                compute_log_likelihood(idata, compile_kwargs={"mode": "NUMBA"})
+        assert len(patched_compile_pymc.call_args_list) == 2
+        assert patched_compile_pymc.call_args_list[0].kwargs["mode"] == "JAX"
+        assert patched_compile_pymc.call_args_list[1].kwargs["mode"] == "NUMBA"