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Consolidate skills
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Timothy Kassis
241
scientific-skills/pymc/assets/linear_regression_template.py
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241
scientific-skills/pymc/assets/linear_regression_template.py
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"""
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PyMC Linear Regression Template
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This template provides a complete workflow for Bayesian linear regression,
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including data preparation, model building, diagnostics, and predictions.
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Customize the sections marked with # TODO
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"""
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import pymc as pm
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import arviz as az
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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# =============================================================================
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# 1. DATA PREPARATION
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# =============================================================================
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# TODO: Load your data
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# Example:
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# df = pd.read_csv('data.csv')
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# X = df[['predictor1', 'predictor2', 'predictor3']].values
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# y = df['outcome'].values
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# For demonstration:
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np.random.seed(42)
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n_samples = 100
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n_predictors = 3
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X = np.random.randn(n_samples, n_predictors)
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true_beta = np.array([1.5, -0.8, 2.1])
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true_alpha = 0.5
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y = true_alpha + X @ true_beta + np.random.randn(n_samples) * 0.5
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# Standardize predictors for better sampling
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X_mean = X.mean(axis=0)
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X_std = X.std(axis=0)
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X_scaled = (X - X_mean) / X_std
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# =============================================================================
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# 2. BUILD MODEL
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# =============================================================================
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# TODO: Customize predictor names
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predictor_names = ['predictor1', 'predictor2', 'predictor3']
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coords = {
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'predictors': predictor_names,
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'obs_id': np.arange(len(y))
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}
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with pm.Model(coords=coords) as linear_model:
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# Priors
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# TODO: Adjust prior parameters based on your domain knowledge
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alpha = pm.Normal('alpha', mu=0, sigma=1)
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beta = pm.Normal('beta', mu=0, sigma=1, dims='predictors')
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sigma = pm.HalfNormal('sigma', sigma=1)
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# Linear predictor
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mu = alpha + pm.math.dot(X_scaled, beta)
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# Likelihood
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y_obs = pm.Normal('y_obs', mu=mu, sigma=sigma, observed=y, dims='obs_id')
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# =============================================================================
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# 3. PRIOR PREDICTIVE CHECK
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# =============================================================================
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print("Running prior predictive check...")
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with linear_model:
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prior_pred = pm.sample_prior_predictive(samples=1000, random_seed=42)
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# Visualize prior predictions
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fig, ax = plt.subplots(figsize=(10, 6))
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az.plot_ppc(prior_pred, group='prior', num_pp_samples=100, ax=ax)
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ax.set_title('Prior Predictive Check')
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plt.tight_layout()
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plt.savefig('prior_predictive_check.png', dpi=300, bbox_inches='tight')
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print("Prior predictive check saved to 'prior_predictive_check.png'")
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# =============================================================================
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# 4. FIT MODEL
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# =============================================================================
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print("\nFitting model...")
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with linear_model:
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# Optional: Quick ADVI exploration
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# approx = pm.fit(n=20000, random_seed=42)
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# MCMC sampling
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idata = pm.sample(
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draws=2000,
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tune=1000,
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chains=4,
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target_accept=0.9,
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random_seed=42,
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idata_kwargs={'log_likelihood': True}
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)
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print("Sampling complete!")
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# =============================================================================
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# 5. CHECK DIAGNOSTICS
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# =============================================================================
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print("\n" + "="*60)
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print("DIAGNOSTICS")
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print("="*60)
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# Summary statistics
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summary = az.summary(idata, var_names=['alpha', 'beta', 'sigma'])
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print("\nParameter Summary:")
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print(summary)
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# Check convergence
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bad_rhat = summary[summary['r_hat'] > 1.01]
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if len(bad_rhat) > 0:
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print(f"\n⚠️ WARNING: {len(bad_rhat)} parameters with R-hat > 1.01")
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print(bad_rhat[['r_hat']])
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else:
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print("\n✓ All R-hat values < 1.01 (good convergence)")
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# Check effective sample size
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low_ess = summary[summary['ess_bulk'] < 400]
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if len(low_ess) > 0:
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print(f"\n⚠️ WARNING: {len(low_ess)} parameters with ESS < 400")
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print(low_ess[['ess_bulk', 'ess_tail']])
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else:
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print("\n✓ All ESS values > 400 (sufficient samples)")
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# Check divergences
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divergences = idata.sample_stats.diverging.sum().item()
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if divergences > 0:
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print(f"\n⚠️ WARNING: {divergences} divergent transitions")
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print(" Consider increasing target_accept or reparameterizing")
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else:
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print("\n✓ No divergences")
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# Trace plots
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fig, axes = plt.subplots(len(['alpha', 'beta', 'sigma']), 2, figsize=(12, 8))
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az.plot_trace(idata, var_names=['alpha', 'beta', 'sigma'], axes=axes)
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plt.tight_layout()
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plt.savefig('trace_plots.png', dpi=300, bbox_inches='tight')
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print("\nTrace plots saved to 'trace_plots.png'")
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# =============================================================================
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# 6. POSTERIOR PREDICTIVE CHECK
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# =============================================================================
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print("\nRunning posterior predictive check...")
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with linear_model:
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pm.sample_posterior_predictive(idata, extend_inferencedata=True, random_seed=42)
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# Visualize fit
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fig, ax = plt.subplots(figsize=(10, 6))
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az.plot_ppc(idata, num_pp_samples=100, ax=ax)
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ax.set_title('Posterior Predictive Check')
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plt.tight_layout()
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plt.savefig('posterior_predictive_check.png', dpi=300, bbox_inches='tight')
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print("Posterior predictive check saved to 'posterior_predictive_check.png'")
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# =============================================================================
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# 7. ANALYZE RESULTS
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# =============================================================================
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# Posterior distributions
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fig, axes = plt.subplots(1, 3, figsize=(15, 4))
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az.plot_posterior(idata, var_names=['alpha', 'beta', 'sigma'], ax=axes)
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plt.tight_layout()
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plt.savefig('posterior_distributions.png', dpi=300, bbox_inches='tight')
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print("Posterior distributions saved to 'posterior_distributions.png'")
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# Forest plot for coefficients
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fig, ax = plt.subplots(figsize=(8, 6))
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az.plot_forest(idata, var_names=['beta'], combined=True, ax=ax)
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ax.set_title('Coefficient Estimates (95% HDI)')
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ax.set_yticklabels(predictor_names)
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plt.tight_layout()
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plt.savefig('coefficient_forest_plot.png', dpi=300, bbox_inches='tight')
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print("Forest plot saved to 'coefficient_forest_plot.png'")
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# Print coefficient estimates
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print("\n" + "="*60)
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print("COEFFICIENT ESTIMATES")
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print("="*60)
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beta_samples = idata.posterior['beta']
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for i, name in enumerate(predictor_names):
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mean = beta_samples.sel(predictors=name).mean().item()
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hdi = az.hdi(beta_samples.sel(predictors=name), hdi_prob=0.95)
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print(f"{name:20s}: {mean:7.3f} [95% HDI: {hdi.values[0]:7.3f}, {hdi.values[1]:7.3f}]")
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# =============================================================================
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# 8. PREDICTIONS FOR NEW DATA
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# =============================================================================
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# TODO: Provide new data for predictions
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# X_new = np.array([[...], [...], ...]) # New predictor values
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# For demonstration, use some test data
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X_new = np.random.randn(10, n_predictors)
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X_new_scaled = (X_new - X_mean) / X_std
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# Update model data and predict
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with linear_model:
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pm.set_data({'X_scaled': X_new_scaled, 'obs_id': np.arange(len(X_new))})
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post_pred = pm.sample_posterior_predictive(
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idata.posterior,
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var_names=['y_obs'],
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random_seed=42
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)
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# Extract predictions
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y_pred_samples = post_pred.posterior_predictive['y_obs']
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y_pred_mean = y_pred_samples.mean(dim=['chain', 'draw']).values
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y_pred_hdi = az.hdi(y_pred_samples, hdi_prob=0.95).values
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print("\n" + "="*60)
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print("PREDICTIONS FOR NEW DATA")
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print("="*60)
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print(f"{'Index':<10} {'Mean':<15} {'95% HDI Lower':<15} {'95% HDI Upper':<15}")
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print("-"*60)
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for i in range(len(X_new)):
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print(f"{i:<10} {y_pred_mean[i]:<15.3f} {y_pred_hdi[i, 0]:<15.3f} {y_pred_hdi[i, 1]:<15.3f}")
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# =============================================================================
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# 9. SAVE RESULTS
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# =============================================================================
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# Save InferenceData
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idata.to_netcdf('linear_regression_results.nc')
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print("\nResults saved to 'linear_regression_results.nc'")
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# Save summary to CSV
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summary.to_csv('model_summary.csv')
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print("Summary saved to 'model_summary.csv'")
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print("\n" + "="*60)
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print("ANALYSIS COMPLETE")
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print("="*60)
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