scientific-bayesian-statistics

Build hierarchical models with partial pooling in PyMC by defining group-level priors and likelihoods, sampling the posterior, and using ArviZ to summarize parameter estimates and varying effects.

Compare Bayesian models using LOO and WAIC by computing information criteria on posterior samples, evaluating out-of-sample predictive accuracy to select the best probabilistic model.

Run posterior predictive checks by simulating replicated data from the posterior predictive distribution and comparing it against observed data using ArviZ visualizations to assess model fit.

Bayesian inference requires diagnostics like Rhat and ESS to verify Markov chain convergence and effective sample size, ensuring posterior parameter estimates from Stan or PyMC are reliable.

You can use Stan for parameter estimation instead of PyMC. Both frameworks support probabilistic modeling and Bayesian inference, allowing you to fit models and evaluate posterior distributions with ArviZ.

Choose priors for Bayesian linear regression based on domain knowledge or weakly informative distributions, which stabilizes parameter estimation and influences posterior summaries during probabilistic modeling.