diff --git a/.github/release.yml b/.github/release.yml
index 236ad7afe..e69d87afe 100644
--- a/.github/release.yml
+++ b/.github/release.yml
@@ -11,6 +11,9 @@ changelog:
     - title: Major Changes 🛠
       labels:
         - major
+    - title: Deprecations 🚨
+      labels:
+        - deprecation
     - title: New Features 🎉
       labels:
         - enhancement
diff --git a/docs/source/notebooks/mmm/mmm_budget_allocation_example.ipynb b/docs/source/notebooks/mmm/mmm_budget_allocation_example.ipynb
index 3ae1fe8d6..4208e1bd3 100644
--- a/docs/source/notebooks/mmm/mmm_budget_allocation_example.ipynb
+++ b/docs/source/notebooks/mmm/mmm_budget_allocation_example.ipynb
@@ -1236,7 +1236,7 @@
     "initial_budget_scenario[\"t\"] = 0\n",
     "\n",
     "response_initial_budget = mmm.sample_posterior_predictive(\n",
-    "    X_pred=initial_budget_scenario, extend_idata=False\n",
+    "    initial_budget_scenario, extend_idata=False\n",
     ")\n",
     "\n",
     "response_initial_budget"
diff --git a/docs/source/notebooks/mmm/mmm_case_study.ipynb b/docs/source/notebooks/mmm/mmm_case_study.ipynb
index 84e1b1cd1..f7cd26c7b 100644
--- a/docs/source/notebooks/mmm/mmm_case_study.ipynb
+++ b/docs/source/notebooks/mmm/mmm_case_study.ipynb
@@ -6285,7 +6285,7 @@
    "outputs": [],
    "source": [
     "y_pred_test = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_test,\n",
+    "    X_test,\n",
     "    include_last_observations=True,\n",
     "    original_scale=True,\n",
     "    var_names=[\"y\", \"channel_contributions\"],\n",
@@ -6942,7 +6942,7 @@
     "    X_actual_uniform[control] = 0.0\n",
     "\n",
     "pred_test_uniform = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_actual_uniform,\n",
+    "    X_actual_uniform,\n",
     "    include_last_observations=True,\n",
     "    original_scale=True,\n",
     "    var_names=[\"y\", \"channel_contributions\"],\n",
diff --git a/docs/source/notebooks/mmm/mmm_counterfactuals.ipynb b/docs/source/notebooks/mmm/mmm_counterfactuals.ipynb
index 2ca34b60f..4efe7cddc 100644
--- a/docs/source/notebooks/mmm/mmm_counterfactuals.ipynb
+++ b/docs/source/notebooks/mmm/mmm_counterfactuals.ipynb
@@ -701,7 +701,7 @@
    ],
    "source": [
     "y_forecast = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_forecast, extend_idata=False, include_last_observations=True\n",
+    "    X_forecast, extend_idata=False, include_last_observations=True\n",
     ")"
    ]
   },
@@ -958,7 +958,7 @@
    ],
    "source": [
     "y_intervention = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_intervention, extend_idata=False, include_last_observations=True\n",
+    "    X_intervention, extend_idata=False, include_last_observations=True\n",
     ")"
    ]
   },
@@ -1289,7 +1289,7 @@
    ],
    "source": [
     "y_counterfactual = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_counterfactual, extend_idata=False\n",
+    "    X_counterfactual, extend_idata=False\n",
     ");"
    ]
   },
diff --git a/docs/source/notebooks/mmm/mmm_example.ipynb b/docs/source/notebooks/mmm/mmm_example.ipynb
index 18115b86d..6e0ffa7ce 100644
--- a/docs/source/notebooks/mmm/mmm_example.ipynb
+++ b/docs/source/notebooks/mmm/mmm_example.ipynb
@@ -9661,7 +9661,7 @@
     "- `sample_posterior_predictive` : Get the full posterior predictive distribution\n",
     "- `predict`: Get the mean of the posterior predictive distribution\n",
     "\n",
-    "These methods take new data, `X_pred`, and some additional `kwargs` for new predictions. Namely, \n",
+    "These methods take new data, `X`, and some additional `kwargs` for new predictions. Namely, \n",
     "\n",
     "- `include_last_observations` : boolean flag in order to carry adstock effects from last observations in the training dataset"
    ]
@@ -10313,9 +10313,7 @@
     }
    ],
    "source": [
-    "y_out_of_sample = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_out_of_sample, extend_idata=False\n",
-    ")\n",
+    "y_out_of_sample = mmm.sample_posterior_predictive(X_out_of_sample, extend_idata=False)\n",
     "\n",
     "y_out_of_sample"
    ]
@@ -10435,7 +10433,7 @@
    ],
    "source": [
     "y_out_of_sample_with_adstock = mmm.sample_posterior_predictive(\n",
-    "    X_pred=X_out_of_sample, extend_idata=False, include_last_observations=True\n",
+    "    X_out_of_sample, extend_idata=False, include_last_observations=True\n",
     ")"
    ]
   },
diff --git a/docs/source/notebooks/mmm/mmm_time_slice_cross_validation.ipynb b/docs/source/notebooks/mmm/mmm_time_slice_cross_validation.ipynb
index 7fd73eba9..02bad2932 100644
--- a/docs/source/notebooks/mmm/mmm_time_slice_cross_validation.ipynb
+++ b/docs/source/notebooks/mmm/mmm_time_slice_cross_validation.ipynb
@@ -260,7 +260,7 @@
     "    mmm = fit_mmm(mmm, X_train, y_train, random_seed)\n",
     "\n",
     "    y_pred_test = mmm.sample_posterior_predictive(\n",
-    "        X_pred=X_test,\n",
+    "        X_test,\n",
     "        include_last_observations=True,\n",
     "        original_scale=True,\n",
     "        extend_idata=False,\n",
diff --git a/docs/source/notebooks/mmm/mmm_tvp_example.ipynb b/docs/source/notebooks/mmm/mmm_tvp_example.ipynb
index f302c6df0..8206ed959 100644
--- a/docs/source/notebooks/mmm/mmm_tvp_example.ipynb
+++ b/docs/source/notebooks/mmm/mmm_tvp_example.ipynb
@@ -613,7 +613,7 @@
                 "    # Sample posterior predictive in whole data range (train and test)\n",
                 "    if \"posterior_predictive\" not in mmm.idata:\n",
                 "        mmm.sample_posterior_predictive(\n",
-                "            X_pred=DATA, extend_idata=True, var_names=[\"y\", \"intercept\"]\n",
+                "            DATA, extend_idata=True, var_names=[\"y\", \"intercept\"]\n",
                 "        )\n",
                 "    mmm.y = target_series.values\n",
                 "\n",
diff --git a/pymc_marketing/mlflow.py b/pymc_marketing/mlflow.py
index e605e610f..e43055f20 100644
--- a/pymc_marketing/mlflow.py
+++ b/pymc_marketing/mlflow.py
@@ -673,7 +673,7 @@ class MMMWrapper(mlflow.pyfunc.PythonModel):
         Combine chain and draw dims into sample. Won't work if a dim named sample already exists. Defaults to True.
     include_last_observations : bool, default=False
         Boolean determining whether to include the last observations of the training data in order to carry over
-        costs with the adstock transformation. Assumes that X_pred are the next predictions following the
+        costs with the adstock transformation. Assumes that X are the next predictions following the
         training data. Defaults to False.
     original_scale : bool, default=True
         Boolean determining whether to return the predictions in the original scale of the target variable.
@@ -800,7 +800,7 @@ def log_mmm(
         already exists. Used for posterior/prior predictive sampling. Defaults to True.
     include_last_observations : bool, optional
         Whether to include the last observations of training data for adstock transformation.
-        Assumes X_pred are next predictions following training data. Used for all prediction
+        Assumes X are next predictions following training data. Used for all prediction
         methods. Defaults to False.
     original_scale : bool, optional
         Whether to return predictions in original scale of target variable. Used for all
diff --git a/pymc_marketing/mmm/hsgp.py b/pymc_marketing/mmm/hsgp.py
index 6aebc89e2..11edd3183 100644
--- a/pymc_marketing/mmm/hsgp.py
+++ b/pymc_marketing/mmm/hsgp.py
@@ -655,10 +655,10 @@ def parameterize_from_data(
         if isinstance(X, np.ndarray):
             numeric_X = np.asarray(X)
         elif isinstance(X, TensorVariable):
-            numeric_X = X.get_value(borrow=False)  # current numeric data
+            numeric_X = X.get_value(borrow=False)
         else:
             raise ValueError(
-                "X must be a NumPy array (or list) or a pm.Data/pm.MutableData. "
+                "X must be a NumPy array (or list) or a TensorVariable. "
                 "If it's a plain symbolic tensor, you must manually specify m, L."
             )
 
@@ -666,9 +666,8 @@ def parameterize_from_data(
         if X_mid is None:
             X_mid = float(numeric_X.mean())
 
-        # 3. Use the standard approximation
         m, L = create_m_and_L_recommendations(
-            numeric_X,  # numeric version
+            numeric_X,
             X_mid,
             ls_lower=ls_lower,
             ls_upper=ls_upper,
diff --git a/pymc_marketing/mmm/mmm.py b/pymc_marketing/mmm/mmm.py
index a3451b8a2..f92147d85 100644
--- a/pymc_marketing/mmm/mmm.py
+++ b/pymc_marketing/mmm/mmm.py
@@ -55,6 +55,7 @@
     create_new_spend_data,
 )
 from pymc_marketing.mmm.validating import ValidateControlColumns
+from pymc_marketing.model_builder import _handle_deprecate_pred_argument
 from pymc_marketing.model_config import parse_model_config
 from pymc_marketing.prior import Prior
 
@@ -1902,7 +1903,7 @@ def legend_title_func(channel):
 
     def sample_posterior_predictive(
         self,
-        X_pred,
+        X=None,
         extend_idata: bool = True,
         combined: bool = True,
         include_last_observations: bool = False,
@@ -1913,7 +1914,7 @@ def sample_posterior_predictive(
 
         Parameters
         ----------
-        X_pred : array, shape (n_pred, n_features)
+        X : array, shape (n_pred, n_features)
             The input data used for prediction.
         extend_idata : bool, optional
             Boolean determining whether the predictions should be added to inference data object. Defaults to True.
@@ -1921,7 +1922,7 @@ def sample_posterior_predictive(
             Combine chain and draw dims into sample. Won't work if a dim named sample already exists. Defaults to True.
         include_last_observations: bool, optional
             Boolean determining whether to include the last observations of the training data in order to carry over
-            costs with the adstock transformation. Assumes that X_pred are the next predictions following the
+            costs with the adstock transformation. Assumes that X are the next predictions following the
             training data.Defaults to False.
         original_scale: bool, optional
             Boolean determining whether to return the predictions in the original scale of the target variable.
@@ -1932,15 +1933,16 @@ def sample_posterior_predictive(
         Returns
         -------
         posterior_predictive_samples : DataArray, shape (n_pred, samples)
-            Posterior predictive samples for each input X_pred
+            Posterior predictive samples for each input X
 
         """
+        X = _handle_deprecate_pred_argument(X, "X", sample_posterior_predictive_kwargs)
         if include_last_observations:
-            X_pred = pd.concat(
-                [self.X.iloc[-self.adstock.l_max :, :], X_pred], axis=0
+            X = pd.concat(
+                [self.X.iloc[-self.adstock.l_max :, :], X], axis=0
             ).sort_values(by=self.date_column)
 
-        self._data_setter(X_pred)
+        self._data_setter(X)
 
         with self.model:  # sample with new input data
             post_pred = pm.sample_posterior_predictive(
@@ -2251,7 +2253,7 @@ def sample_response_distribution(
         constant_data = allocation_strategy.to_dataset(name="allocation")
 
         return self.sample_posterior_predictive(
-            X_pred=synth_dataset,
+            X=synth_dataset,
             extend_idata=False,
             include_last_observations=True,
             original_scale=False,
diff --git a/pymc_marketing/model_builder.py b/pymc_marketing/model_builder.py
index 7cc224121..6f11c588f 100644
--- a/pymc_marketing/model_builder.py
+++ b/pymc_marketing/model_builder.py
@@ -46,6 +46,33 @@ def check_array(X, **kwargs):
         return X
 
 
+def _handle_deprecate_pred_argument(
+    value,
+    name: str,
+    kwargs: dict,
+    none_allowed: bool = False,
+):
+    name_pred = f"{name}_pred"
+    if name_pred in kwargs and value is not None:
+        raise ValueError(f"Both {name} and {name_pred} cannot be provided.")
+
+    if name_pred not in kwargs and value is None and none_allowed:
+        return value
+
+    if name_pred not in kwargs and value is None:
+        raise ValueError(f"Please provide {name}.")
+
+    if name_pred in kwargs:
+        warnings.warn(
+            f"{name_pred} is deprecated, use {name} instead",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        return kwargs.pop(name_pred)
+
+    return value
+
+
 def create_idata_accessor(value: str, message: str):
     """Create a property accessor for an InferenceData object.
 
@@ -634,7 +661,6 @@ def fit(
         X: pd.DataFrame,
         y: pd.Series | np.ndarray | None = None,
         progressbar: bool | None = None,
-        predictor_names: list[str] | None = None,
         random_seed: RandomState | None = None,
         **kwargs: Any,
     ) -> az.InferenceData:
@@ -650,10 +676,6 @@ def fit(
             The target values (real numbers). If scikit-learn is available, array-like, otherwise array.
         progressbar : bool, optional
             Specifies whether the fit progress bar should be displayed. Defaults to True.
-        predictor_names : Optional[List[str]] = None,
-            Allows for custom naming of predictors when given in a form of a 2D array.
-            Allows for naming of predictors when given in a form of np.ndarray, if not provided
-            the predictors will be named like predictor1, predictor2...
         random_seed : Optional[RandomState]
             Provides sampler with initial random seed for obtaining reproducible samples.
         **kwargs : Any
@@ -675,8 +697,6 @@ def fit(
         if isinstance(y, pd.Series) and not X.index.equals(y.index):
             raise ValueError("Index of X and y must match.")
 
-        if predictor_names is None:
-            predictor_names = []
         if y is None:
             y = np.zeros(X.shape[0])
 
@@ -763,7 +783,7 @@ def fit_result(self, res: az.InferenceData) -> None:
 
     def predict(
         self,
-        X_pred: np.ndarray | pd.DataFrame | pd.Series,
+        X: np.ndarray | pd.DataFrame | pd.Series | None = None,
         extend_idata: bool = True,
         **kwargs,
     ) -> np.ndarray:
@@ -773,7 +793,7 @@ def predict(
 
         Parameters
         ----------
-        X_pred : array-like | array, shape (n_pred, n_features)
+        X : array-like | array, shape (n_pred, n_features)
             The input data used for prediction. If scikit-learn is available, array-like, otherwise array.
         extend_idata : Boolean
             Determine whether the predictions should be added to inference data object.
@@ -782,8 +802,8 @@ def predict(
 
         Returns
         -------
-        y_pred : ndarray, shape (n_pred,)
-            Predicted output corresponding to input X_pred.
+        ndarray, shape (n_pred,)
+            Predicted output corresponding to input X.
 
         Examples
         --------
@@ -795,7 +815,10 @@ def predict(
 
         """
         posterior_predictive_samples = self.sample_posterior_predictive(
-            X_pred, extend_idata, combined=False, **kwargs
+            X,
+            extend_idata=extend_idata,
+            combined=False,
+            **kwargs,
         )
 
         if self.output_var not in posterior_predictive_samples:
@@ -810,8 +833,8 @@ def predict(
 
     def sample_prior_predictive(
         self,
-        X_pred,
-        y_pred=None,
+        X=None,
+        y=None,
         samples: int | None = None,
         extend_idata: bool = True,
         combined: bool = True,
@@ -821,8 +844,11 @@ def sample_prior_predictive(
 
         Parameters
         ----------
-        X_pred : array, shape (n_pred, n_features)
+        X : array, shape (n_pred, n_features)
             The input data used for prediction using prior distribution.
+        y : array, shape (n_pred,), optional
+            The target values (real numbers) used for prediction using prior distribution.
+            If not set, defaults to an array of zeros.
         samples : int
             Number of samples from the prior parameter distributions to generate.
             If not set, uses sampler_config['draws'] if that is available, otherwise defaults to 500.
@@ -837,16 +863,19 @@ def sample_prior_predictive(
         Returns
         -------
         prior_predictive_samples : DataArray, shape (n_pred, samples)
-            Prior predictive samples for each input X_pred
+            Prior predictive samples for each input X
 
         """
-        if y_pred is None:
-            y_pred = np.zeros(len(X_pred))
+        X = _handle_deprecate_pred_argument(X, "X", kwargs)
+        y = _handle_deprecate_pred_argument(y, "y", kwargs, none_allowed=True)
+
+        if y is None:
+            y = np.zeros(len(X))
         if samples is None:
             samples = self.sampler_config.get("draws", 500)
 
         if not hasattr(self, "model"):
-            self.build_model(X_pred, y_pred)
+            self.build_model(X, y)
 
         with self.model:  # sample with new input data
             prior_pred: az.InferenceData = pm.sample_prior_predictive(samples, **kwargs)
@@ -866,7 +895,7 @@ def sample_prior_predictive(
 
     def sample_posterior_predictive(
         self,
-        X_pred,
+        X=None,
         extend_idata: bool = True,
         combined: bool = True,
         **sample_posterior_predictive_kwargs,
@@ -875,7 +904,7 @@ def sample_posterior_predictive(
 
         Parameters
         ----------
-        X_pred : array, shape (n_pred, n_features)
+        X : array, shape (n_pred, n_features)
             The input data used for prediction using prior distribution..
         extend_idata : Boolean
             Determine whether the predictions should be added to inference data object.
@@ -888,10 +917,12 @@ def sample_posterior_predictive(
         Returns
         -------
         posterior_predictive_samples : DataArray, shape (n_pred, samples)
-            Posterior predictive samples for each input X_pred
+            Posterior predictive samples for each input X
 
         """
-        self._data_setter(X_pred)
+        X = _handle_deprecate_pred_argument(X, "X", sample_posterior_predictive_kwargs)
+
+        self._data_setter(X)
 
         with self.model:
             post_pred = pm.sample_posterior_predictive(
@@ -909,18 +940,6 @@ def sample_posterior_predictive(
 
         return az.extract(post_pred, variable_name, combined=combined)
 
-    def get_params(self, deep=True):
-        """Get all the model parameters needed to instantiate a copy of the model, not including training data."""
-        return {
-            "model_config": self.model_config,
-            "sampler_config": self.sampler_config,
-        }
-
-    def set_params(self, **params):
-        """Set all the model parameters needed to instantiate the model, not including training data."""
-        self.model_config = params["model_config"]
-        self.sampler_config = params["sampler_config"]
-
     @property
     @abstractmethod
     def _serializable_model_config(self) -> dict[str, int | float | dict]:
@@ -937,17 +956,17 @@ def _serializable_model_config(self) -> dict[str, int | float | dict]:
 
     def predict_proba(
         self,
-        X_pred: np.ndarray | pd.DataFrame | pd.Series,
+        X: np.ndarray | pd.DataFrame | pd.Series | None = None,
         extend_idata: bool = True,
         combined: bool = False,
         **kwargs,
     ) -> xr.DataArray:
         """Alias for `predict_posterior`, for consistency with scikit-learn probabilistic estimators."""
-        return self.predict_posterior(X_pred, extend_idata, combined, **kwargs)
+        return self.predict_posterior(X, extend_idata, combined, **kwargs)
 
     def predict_posterior(
         self,
-        X_pred: np.ndarray | pd.DataFrame | pd.Series,
+        X: np.ndarray | pd.DataFrame | pd.Series | None = None,
         extend_idata: bool = True,
         combined: bool = True,
         **kwargs,
@@ -956,7 +975,7 @@ def predict_posterior(
 
         Parameters
         ----------
-        X_pred : array-like | array, shape (n_pred, n_features)
+        X : array-like | array, shape (n_pred, n_features)
             The input data used for prediction. If scikit-learn is available, array-like, otherwise array.
         extend_idata : Boolean
             Determine whether the predictions should be added to inference data object.
@@ -969,13 +988,14 @@ def predict_posterior(
         Returns
         -------
         y_pred : DataArray
-            Posterior predictive samples for each input X_pred.
+            Posterior predictive samples for each input X.
             Shape is (n_pred, chains * draws) if combined is True, otherwise (chains, draws, n_pred).
 
         """
-        X_pred = self._validate_data(X_pred)
+        X = _handle_deprecate_pred_argument(X, "X", kwargs)
+        X = self._validate_data(X)
         posterior_predictive_samples = self.sample_posterior_predictive(
-            X_pred, extend_idata, combined, **kwargs
+            X, extend_idata, combined, **kwargs
         )
 
         if self.output_var not in posterior_predictive_samples:
diff --git a/tests/mmm/test_hsgp.py b/tests/mmm/test_hsgp.py
index 6ddf43f3b..06577123e 100644
--- a/tests/mmm/test_hsgp.py
+++ b/tests/mmm/test_hsgp.py
@@ -13,6 +13,8 @@
 #   limitations under the License.
 import matplotlib.pyplot as plt
 import numpy as np
+import pymc as pm
+import pytensor
 import pytensor.tensor as pt
 import pytest
 import xarray as xr
@@ -307,3 +309,41 @@ def test_from_dict_with_non_dictionary_distribution_hspg_periodic() -> None:
     assert hsgp.scale == 1
     assert hsgp.X_mid is None
     assert hsgp.dims == ("time",)
+
+
+def test_hsgp_with_shared_data():
+    """
+    Test that HSGP works with a shared variable (pm.MutableData / pm.Data) and that
+    the computed graph properly includes and depends on the shared data.
+    """
+    n_points = 10
+    X = np.arange(n_points, dtype=float)
+    coords = {"time": X}
+
+    # Create a model and a shared data variable using pm.MutableData
+    with pm.Model(coords=coords) as model:
+        # Create a shared data variable with the name "X_shared"
+        X_shared = pm.Data("X_shared", X, dims="time")
+        # Parameterize the HSGP using the shared data
+        hsgp = HSGP.parameterize_from_data(X_shared, dims="time")
+        # Create the deterministic variable "f" from the HSGP configuration
+        f = hsgp.create_variable("f")
+
+        # Check that "f" is added to the model variables
+        assert "f" in model.named_vars
+
+        # Ensure that the stored X is a shared tensor variable
+        assert isinstance(hsgp.X, pt.TensorVariable)
+
+        # Verify that f depends on X_shared in the computational graph
+        assert any(
+            var.name == "X_shared"
+            for var in pytensor.graph.basic.ancestors([f])
+            if hasattr(var, "name")
+        ), "f is not connected to X_shared in the computational graph"
+
+        # Sample from prior to get initial values
+        prior = pm.sample_prior_predictive(samples=1)
+
+        # prior should have a "f" variable
+        assert "f" in prior.prior
diff --git a/tests/mmm/test_mmm.py b/tests/mmm/test_mmm.py
index 226a861da..fb56e480e 100644
--- a/tests/mmm/test_mmm.py
+++ b/tests/mmm/test_mmm.py
@@ -1063,10 +1063,10 @@ def test_new_data_sample_posterior_predictive_method(
 ) -> None:
     """This is the method that is used in all the other methods that generate predictions."""
     mmm = request.getfixturevalue(model_name)
-    X_pred = generate_data(new_dates)
+    X = generate_data(new_dates)
 
     posterior_predictive = mmm.sample_posterior_predictive(
-        X_pred=X_pred,
+        X=X,
         extend_idata=False,
         combined=combined,
         original_scale=original_scale,
@@ -1087,10 +1087,10 @@ def test_sample_posterior_predictive_with_prediction_kwarg(
     predictions: bool,
 ) -> None:
     new_dates = pd.date_range("2022-01-01", "2022-03-01", freq="W-MON")
-    X_pred = generate_data(new_dates)
+    X = generate_data(new_dates)
 
     predictions = mmm_fitted.sample_posterior_predictive(
-        X_pred=X_pred,
+        X=X,
         extend_idata=False,
         combined=True,
         predictions=predictions,
@@ -1115,14 +1115,14 @@ def test_new_data_include_last_observation_same_dims(
     request,
 ) -> None:
     mmm = request.getfixturevalue(model_name)
-    X_pred = generate_data(new_dates)
+    X = generate_data(new_dates)
 
     pp_without = mmm.predict_posterior(
-        X_pred,
+        X,
         include_last_observations=False,
     )
     pp_with = mmm.predict_posterior(
-        X_pred,
+        X,
         include_last_observations=True,
     )
 
@@ -1148,9 +1148,9 @@ def test_new_data_predict_method(
     request,
 ) -> None:
     mmm = request.getfixturevalue(model_name)
-    X_pred = generate_data(new_dates)
+    X = generate_data(new_dates)
 
-    posterior_predictive_mean = mmm.predict(X_pred=X_pred)
+    posterior_predictive_mean = mmm.predict(X=X)
 
     assert isinstance(posterior_predictive_mean, np.ndarray)
     assert posterior_predictive_mean.shape[0] == new_dates.size
@@ -1202,7 +1202,7 @@ def test_new_spend_contributions_prior_error() -> None:
 @pytest.mark.parametrize("original_scale", [True, False])
 def test_new_spend_contributions_prior(original_scale, mmm, toy_X) -> None:
     mmm.sample_prior_predictive(
-        X_pred=toy_X,
+        X=toy_X,
         extend_idata=True,
     )
 
diff --git a/tests/test_model_builder.py b/tests/test_model_builder.py
index 4a05364e1..3630e3709 100644
--- a/tests/test_model_builder.py
+++ b/tests/test_model_builder.py
@@ -358,7 +358,7 @@ def test_sample_xxx_predictive_keeps_second(
     X_pred = toy_X
 
     kwargs = {
-        "X_pred": X_pred,
+        "X": X_pred,
         "combined": False,
         "extend_idata": True,
         "random_seed": rng,
@@ -457,7 +457,7 @@ def test_insufficient_attrs() -> None:
 
     match = "__init__ has parameters that are not in the attrs"
     with pytest.raises(ValueError, match=match):
-        model.sample_prior_predictive(X_pred=X_pred)
+        model.sample_prior_predictive(X=X_pred)
 
 
 def test_incorrect_set_idata_attrs_override() -> None:
@@ -471,7 +471,7 @@ def create_idata_attrs(self) -> dict:
 
     match = "Missing required keys in attrs"
     with pytest.raises(ValueError, match=match):
-        model.sample_prior_predictive(X_pred=X_pred)
+        model.sample_prior_predictive(X=X_pred)
 
 
 @pytest.mark.parametrize(
@@ -618,3 +618,41 @@ def test_graphviz(toy_X, toy_y):
 
     model.build_model(X=toy_X, y=toy_y)
     assert isinstance(model.graphviz(), graphviz.graphs.Digraph)
+
+
+@pytest.mark.parametrize(
+    "method_name",
+    [
+        "sample_posterior_predictive",
+        "predict",
+    ],
+)
+def test_X_pred_posterior_deprecation(
+    method_name,
+    fitted_model_instance,
+    toy_X,
+) -> None:
+    if "posterior_predictive" in fitted_model_instance.idata:
+        del fitted_model_instance.idata.posterior_predictive
+
+    with pytest.warns(DeprecationWarning, match="X_pred is deprecated"):
+        method = getattr(fitted_model_instance, method_name)
+        method(X_pred=toy_X)
+
+    assert isinstance(fitted_model_instance.posterior_predictive, xr.Dataset)
+
+
+def test_X_pred_prior_deprecation(fitted_model_instance, toy_X, toy_y) -> None:
+    if "prior" in fitted_model_instance.idata:
+        del fitted_model_instance.idata.prior
+    if "prior_predictive" in fitted_model_instance.idata:
+        del fitted_model_instance.idata.prior_predictive
+
+    with pytest.warns(DeprecationWarning, match="X_pred is deprecated"):
+        fitted_model_instance.sample_prior_predictive(X_pred=toy_X)
+
+    with pytest.warns(DeprecationWarning, match="y_pred is deprecated"):
+        fitted_model_instance.sample_prior_predictive(toy_X, y_pred=toy_y)
+
+    assert isinstance(fitted_model_instance.prior, xr.Dataset)
+    assert isinstance(fitted_model_instance.prior_predictive, xr.Dataset)