Probabilistic Churn Prediction with Bayesian Inference

Develop a Python-based probabilistic churn prediction model using Bayesian statistical methods. The script should integrate multiple data sources (transactional, behavioral, demographic) and implement a hierarchical Bayesian model that calculates individual churn probabilities with credible intervals. Include Monte Carlo simulation to estimate uncertainty, and generate a visualization that shows churn risk stratification with confidence bands. Implement model diagnostics and posterior predictive checks.