"""
PyMC Model Comparison Script
Utilities for comparing multiple Bayesian models using information criteria
and cross-validation metrics.
Usage:
from scripts.model_comparison import compare_models, plot_model_comparison
# Compare multiple models
comparison = compare_models(
{'model1': idata1, 'model2': idata2, 'model3': idata3},
ic='loo'
)
# Visualize comparison
plot_model_comparison(comparison, output_path='model_comparison.png')
"""
import arviz as az
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from typing import Dict
def compare_models(models_dict: Dict[str, az.InferenceData],
ic='loo',
scale='deviance',
verbose=True):
"""
Compare multiple models using information criteria.
Parameters
----------
models_dict : dict
Dictionary mapping model names to InferenceData objects.
All models must have log_likelihood computed.
ic : str
Information criterion to use: 'loo' (default) or 'waic'
scale : str
Scale for IC: 'deviance' (default), 'log', or 'negative_log'
verbose : bool
Print detailed comparison results (default: True)
Returns
-------
pd.DataFrame
Comparison DataFrame with model rankings and statistics
Notes
-----
Models must be fit with idata_kwargs={'log_likelihood': True} or
log-likelihood computed afterwards with pm.compute_log_likelihood().
"""
if verbose:
print("="*70)
print(f" " * 25 + f"MODEL COMPARISON ({ic.upper()})")
print("="*70)
# Perform comparison
comparison = az.compare(models_dict, ic=ic, scale=scale)
if verbose:
print("\nModel Rankings:")
print("-"*70)
print(comparison.to_string())
print("\n" + "="*70)
print("INTERPRETATION GUIDE")
print("="*70)
print(f"• rank: Model ranking (0 = best)")
print(f"• {ic}: {ic.upper()} estimate (lower is better)")
print(f"• p_{ic}: Effective number of parameters")
print(f"• d{ic}: Difference from best model")
print(f"• weight: Model probability (pseudo-BMA)")
print(f"• se: Standard error of {ic.upper()}")
print(f"• dse: Standard error of the difference")
print(f"• warning: True if model has reliability issues")
print(f"• scale: {scale}")
print("\n" + "="*70)
print("MODEL SELECTION GUIDELINES")
print("="*70)
best_model = comparison.index[0]
print(f"\n✓ Best model: {best_model}")
# Check for clear winner
if len(comparison) > 1:
delta = comparison.iloc[1][f'd{ic}']
delta_se = comparison.iloc[1]['dse']
if delta > 10:
print(f" → STRONG evidence for {best_model} (Δ{ic} > 10)")
elif delta > 4:
print(f" → MODERATE evidence for {best_model} (4 < Δ{ic} < 10)")
elif delta > 2:
print(f" → WEAK evidence for {best_model} (2 < Δ{ic} < 4)")
else:
print(f" → Models are SIMILAR (Δ{ic} < 2)")
print(f" Consider model averaging or choose based on simplicity")
# Check if difference is significant relative to SE
if delta > 2 * delta_se:
print(f" → Difference is > 2 SE, likely reliable")
else:
print(f" → Difference is < 2 SE, uncertain distinction")
# Check for warnings
if comparison['warning'].any():
print("\n⚠️ WARNING: Some models have reliability issues")
warned_models = comparison[comparison['warning']].index.tolist()
print(f" Models with warnings: {', '.join(warned_models)}")
print(f" → Check Pareto-k diagnostics with check_loo_reliability()")
return comparison
def check_loo_reliability(models_dict: Dict[str, az.InferenceData],
threshold=0.7,
verbose=True):
"""
Check LOO-CV reliability using Pareto-k diagnostics.
Parameters
----------
models_dict : dict
Dictionary mapping model names to InferenceData objects
threshold : float
Pareto-k threshold for flagging observations (default: 0.7)
verbose : bool
Print detailed diagnostics (default: True)
Returns
-------
dict
Dictionary with Pareto-k diagnostics for each model
"""
if verbose:
print("="*70)
print(" " * 20 + "LOO RELIABILITY CHECK")
print("="*70)
results = {}
for name, idata in models_dict.items():
if verbose:
print(f"\n{name}:")
print("-"*70)
# Compute LOO with pointwise results
loo_result = az.loo(idata, pointwise=True)
pareto_k = loo_result.pareto_k.values
# Count problematic observations
n_high = (pareto_k > threshold).sum()
n_very_high = (pareto_k > 1.0).sum()
results[name] = {
'pareto_k': pareto_k,
'n_high': n_high,
'n_very_high': n_very_high,
'max_k': pareto_k.max(),
'loo': loo_result
}
if verbose:
print(f"Pareto-k diagnostics:")
print(f" • Good (k < 0.5): {(pareto_k < 0.5).sum()} observations")
print(f" • OK (0.5 ≤ k < 0.7): {((pareto_k >= 0.5) & (pareto_k < 0.7)).sum()} observations")
print(f" • Bad (0.7 ≤ k < 1.0): {((pareto_k >= 0.7) & (pareto_k < 1.0)).sum()} observations")
print(f" • Very bad (k ≥ 1.0): {(pareto_k >= 1.0).sum()} observations")
print(f" • Maximum k: {pareto_k.max():.3f}")
if n_high > 0:
print(f"\n⚠️ {n_high} observations with k > {threshold}")
print(" LOO approximation may be unreliable for these points")
print(" Solutions:")
print(" → Use WAIC instead (less sensitive to outliers)")
print(" → Investigate influential observations")
print(" → Consider more flexible model")
if n_very_high > 0:
print(f"\n⚠️ {n_very_high} observations with k > 1.0")
print(" These points have very high influence")
print(" → Strongly consider K-fold CV or other validation")
else:
print(f"✓ All Pareto-k values < {threshold}")
print(" LOO estimates are reliable")
return results
def plot_model_comparison(comparison, output_path=None, show=True):
"""
Visualize model comparison results.
Parameters
----------
comparison : pd.DataFrame
Comparison DataFrame from az.compare()
output_path : str, optional
If provided, save plot to this path
show : bool
Whether to display plot (default: True)
Returns
-------
matplotlib.figure.Figure
The comparison figure
"""
fig = plt.figure(figsize=(10, 6))
az.plot_compare(comparison)
plt.title('Model Comparison', fontsize=14, fontweight='bold')
plt.tight_layout()
if output_path:
plt.savefig(output_path, dpi=300, bbox_inches='tight')
print(f"Comparison plot saved to {output_path}")
if show:
plt.show()
else:
plt.close()
return fig
def model_averaging(models_dict: Dict[str, az.InferenceData],
weights=None,
var_name='y_obs',
ic='loo'):
"""
Perform Bayesian model averaging using model weights.
Parameters
----------
models_dict : dict
Dictionary mapping model names to InferenceData objects
weights : array-like, optional
Model weights. If None, computed from IC (pseudo-BMA weights)
var_name : str
Name of the predicted variable (default: 'y_obs')
ic : str
Information criterion for computing weights if not provided
Returns
-------
np.ndarray
Averaged predictions across models
np.ndarray
Model weights used
"""
if weights is None:
comparison = az.compare(models_dict, ic=ic)
weights = comparison['weight'].values
model_names = comparison.index.tolist()
else:
model_names = list(models_dict.keys())
weights = np.array(weights)
weights = weights / weights.sum() # Normalize
print("="*70)
print(" " * 22 + "BAYESIAN MODEL AVERAGING")
print("="*70)
print("\nModel weights:")
for name, weight in zip(model_names, weights):
print(f" {name}: {weight:.4f} ({weight*100:.2f}%)")
# Extract predictions and average
predictions = []
for name in model_names:
idata = models_dict[name]
if 'posterior_predictive' in idata:
pred = idata.posterior_predictive[var_name].values
else:
print(f"Warning: {name} missing posterior_predictive, skipping")
continue
predictions.append(pred)
# Weighted average
averaged = sum(w * p for w, p in zip(weights, predictions))
print(f"\n✓ Model averaging complete")
print(f" Combined predictions using {len(predictions)} models")
return averaged, weights
def cross_validation_comparison(models_dict: Dict[str, az.InferenceData],
k=10,
verbose=True):
"""
Perform k-fold cross-validation comparison (conceptual guide).
Note: This function provides guidance. Full k-fold CV requires
re-fitting models k times, which should be done in the main script.
Parameters
----------
models_dict : dict
Dictionary of model names to InferenceData
k : int
Number of folds (default: 10)
verbose : bool
Print guidance
Returns
-------
None
"""
if verbose:
print("="*70)
print(" " * 20 + "K-FOLD CROSS-VALIDATION GUIDE")
print("="*70)
print(f"\nTo perform {k}-fold CV:")
print("""
1. Split data into k folds
2. For each fold:
- Train all models on k-1 folds
- Compute log-likelihood on held-out fold
3. Sum log-likelihoods across folds for each model
4. Compare models using total CV score
Example code:
-------------
from sklearn.model_selection import KFold
kf = KFold(n_splits=k, shuffle=True, random_seed=42)
cv_scores = {name: [] for name in models_dict.keys()}
for train_idx, test_idx in kf.split(X):
X_train, X_test = X[train_idx], X[test_idx]
y_train, y_test = y[train_idx], y[test_idx]
for name in models_dict.keys():
# Fit model on train set
with create_model(name, X_train, y_train) as model:
idata = pm.sample()
# Compute log-likelihood on test set
with model:
pm.set_data({'X': X_test, 'y': y_test})
log_lik = pm.compute_log_likelihood(idata).sum()
cv_scores[name].append(log_lik)
# Compare total CV scores
for name, scores in cv_scores.items():
print(f"{name}: {np.sum(scores):.2f}")
""")
print("\nNote: K-fold CV is expensive but most reliable for model comparison")
print(" Use when LOO has reliability issues (high Pareto-k values)")
# Example usage
if __name__ == '__main__':
print("This script provides model comparison utilities for PyMC.")
print("\nExample usage:")
print("""
import pymc as pm
from scripts.model_comparison import compare_models, check_loo_reliability
# Fit multiple models (must include log_likelihood)
with pm.Model() as model1:
# ... define model 1 ...
idata1 = pm.sample(idata_kwargs={'log_likelihood': True})
with pm.Model() as model2:
# ... define model 2 ...
idata2 = pm.sample(idata_kwargs={'log_likelihood': True})
# Compare models
models = {'Simple': idata1, 'Complex': idata2}
comparison = compare_models(models, ic='loo')
# Check reliability
reliability = check_loo_reliability(models)
# Visualize
plot_model_comparison(comparison, output_path='comparison.png')
# Model averaging
averaged_pred, weights = model_averaging(models, var_name='y_obs')
""")