pymc

Bayesian regression models are built by specifying priors and likelihoods to infer posterior distributions from noisy data. You fit the model using MCMC NUTS or ADVI, then interpret the resulting posterior distributions to quantify uncertainty in your predictions.

Bayesian models are validated using posterior predictive checks and convergence diagnostics like R-hat, ESS, and divergences. Model comparison leverages log-likelihood to calculate LOO or WAIC scores, providing statistically grounded metrics to evaluate and select the best performing model.

Hierarchical and multilevel regression workflows are fully supported using modern modeling APIs. You can define grouped structures, fit them with MCMC or variational inference, and handle complex use cases including robust likelihoods, missing data, and measurement error.

MCMC NUTS convergence requires checking diagnostics such as R-hat, ESS, and divergences. Running these checks ensures the posterior distributions are statistically valid, which is essential before performing posterior predictive checks or model comparison.

Pandas and numpy are sufficient for structuring input data arrays before specifying priors and likelihoods. Matplotlib and arviz are also required for visually validating convergence diagnostics and posterior predictive checks after fitting the model.