pymc

To build and validate Bayesian models with MCMC, define probabilistic structures using PyMC, fit them using NUTS sampling, and evaluate results via posterior predictive checks and diagnostics. This workflow quantifies uncertainty for principled decision making.

Hierarchical modeling fits complex group-structured data by estimating varying effects across multiple levels. Non-centered parameterization is used within this probabilistic modeling approach to improve MCMC sampling efficiency and avoid divergences in hierarchical models.

Compare competing Bayesian models using LOO or WAIC by computing information criteria from posterior distributions. These model comparison techniques estimate out-of-sample predictive accuracy to help select the most robust statistical explanation for your data.

Yes, PyMC supports variational inference alongside MCMC sampling for scalable Bayesian inference. Variational inference provides faster approximate posterior estimates, making probabilistic modeling feasible for larger datasets where traditional MCMC is computationally expensive.

The best way to run posterior predictive checks after MCMC sampling is to generate replicated data from the fitted posterior distribution and compare its distribution against observed data. This validates Bayesian model fit and reveals systematic discrepancies.

Yes, you can use ArviZ with PyMC for Bayesian diagnostics and visualizations. ArviZ processes posterior distributions and inference data generated by PyMC's MCMC and variational inference workflows to produce trace plots, diagnostic summaries, and model comparison metrics.