Refactor and enhance SensitivityAnalysis for MMM (#1899)

* Refactor and enhance SensitivityAnalysis for MMM

Expanded SensitivityAnalysis to support arbitrary PyMC models, improved documentation with usage examples, and added flexible sweep and filtering logic. The class now works directly with PyMC models and InferenceData, supports multi-dimensional inputs, and provides Jacobian-based marginal effects with optional xarray output and idata extension. Legacy code using pandas was removed in favor of a more general and robust approach.

* changes

* Applying Erik feedback

* Refactor MMM sensitivity analysis and update tests

Updated sensitivity analysis logic in pymc_marketing/mmm/sensitivity_analysis.py and related plotting in plot.py. Adjusted notebook outputs and execution counts for reproducibility. Modified tests to align with new sensitivity analysis behavior.

* Update

* Changes

* Feedback from team

* Changes requested by Ben

* Avoid the use of nutpie

* Remove warning

---------

Co-authored-by: Juan Orduz <[email protected]>
Co-authored-by: Benjamin T. Vincent <[email protected]>

Author: 3 people

docs/source/notebooks/mmm/mmm_sensitivity_analysis.ipynb

@@ -1713,7 +1713,10 @@ def sensitivity(self) -> SensitivityAnalysis:
         ...     sweep_type="multiplicative",
         ... )
         """
-        return SensitivityAnalysis(mmm=self)
+        # Provide the underlying PyMC model, the model's inference data, and dims
+        return SensitivityAnalysis(
+            pymc_model=self.model, idata=self.idata, dims=self.dims
+        )
 
     def _make_channel_transform(
         self, df_lift_test: pd.DataFrame