adding demo notebook

Signed-off-by: Nathaniel <[email protected]>

Author: NathanielF

causalpy/experiments/instrumental_variable.py

@@ -91,6 +91,16 @@ class InstrumentalVariable(BaseExperiment):
     ...     formula=formula,
     ...     model=InstrumentalVariableRegression(sample_kwargs=sample_kwargs),
     ... )
+    >>> # With variable selection
+    >>> iv = cp.InstrumentalVariable(
+    ...     instruments_data=instruments_data,
+    ...     data=data,
+    ...     instruments_formula=instruments_formula,
+    ...     formula=formula,
+    ...     model=InstrumentalVariableRegression(sample_kwargs=sample_kwargs),
+    ...     vs_prior_type="spike_and_slab",
+    ...     vs_hyperparams={"slab_sigma": 5.0},
+    ... )
     """
 
     supports_ols = False
@@ -115,7 +125,7 @@ def __init__(
         self.formula = formula
         self.instruments_formula = instruments_formula
         self.model = model
-        self.vs_prior_type = (vs_prior_type,)
+        self.vs_prior_type = vs_prior_type
         self.vs_hyperparams = vs_hyperparams or {}
         self.input_validation()
 
@@ -142,7 +152,7 @@ def __init__(
         if priors is None:
             priors = {
                 "mus": [self.ols_beta_first_params, self.ols_beta_second_params],
-                "sigmas": [1, 1],
+                "sigmas": [10, 10],
                 "eta": 2,
                 "lkj_sd": 1,
             }

causalpy/pymc_models.py

@@ -13,6 +13,7 @@
 #   limitations under the License.
 """Custom PyMC models for causal inference"""
 
+import warnings
 from typing import Any, Dict
 
 import arviz as az
@@ -694,6 +695,13 @@ def build_model(  # type: ignore
         with self:
             self.add_coords(coords)
 
+            if vs_prior_type and ("mus" in priors or "sigmas" in priors):
+                warnings.warn(
+                    "Variable selection priors specified. "
+                    "The 'mus' and 'sigmas' in the priors dict will be ignored "
+                    "for beta coefficients. Only 'eta' and 'lkj_sd' will be used."
+                )
+
             # Create coefficient priors
             if vs_prior_type:
                 # Use variable selection priors