pymc-bayesian-modelinglisted

# PyMC Bayesian Modeling ## Overview PyMC is a Python library for Bayesian modeling and probabilistic programming. Build, fit, validate, and compare Bayesian models using PyMC's modern API (version 5.x+), including hierarchical models, MCMC sampling (NUTS), variational inference, and model comparison (LOO, WAIC). ## When to Use This Skill This skill should be used when: - Building Bayesian models (linear/logistic regression, hierarchical models, time series, etc.) - Performing MCMC sampling or variational inference - Conducting prior/posterior predictive checks - Diagnosing sampling issues (divergences, convergence, ESS) - Comparing multiple models using information criteria (LOO, WAIC) - Implementing uncertainty quantification through Bayesian methods - Working with hierarchical/multilevel data structures - Handling missing data or measurement error in a principled way ## Standard Bayesian Workflow Follow this workflow for building and validating Bayesian models: ### 1. Data Preparation ```python import pymc as pm import arviz as az import numpy as np # Load and prepare data X = ... # Predictors y = ... # Outcomes # Standardize predictors for better sampling X_mean = X.mean(axis=0) X_std = X.std(axis=0) X_scaled = (X - X_mean) / X_std ``` **Key practices:** - Standardize continuous predictors (improves sampling efficiency) - Center outcomes when possible - Handle missing data explicitly (treat as parameters) - Use named dimensions with `coords` for clarity ###