Bayesian Inference

3 Credits · Level: Graduate

This course examines essential aspects of the Bayesian approach. It includes Bayes theorem, decision theory, likelihood principles, exchangeability, de Finetti’s theorem, selection of prior distributions (conjugate, non-conjugate, reference), single-parameter models (binomial, poisson, normal), multi-parameter models (normal, multinomial, linear regression, general linear model, hierarchical regression), inference (exact, normal approximations, non-normal iterative approximations), computation (Monte Carlo, convergence diagnostics), and model diagnostics (Bayes factors, posterior predictive checks) as well as the Bayesian approaches to a variety of Biostatistics models using the inverse Bayes theorem related non-iterative sampling and MCMC.