Bayesian Generalized Linear Models: Theory, Computation, and Applications

Bayesian methods provide a flexible and powerful framework for generalized linear models (GLMs), enabling modeling of binary, count, and categorical outcomes while incorporating prior knowledge and fully quantifying uncertainty. This half-day short course offers a focused introduction to Bayesian GLMs, integrating theory, computation, and applied case studies in a concise format. Participants will learn how to specify and interpret Bayesian GLMs, construct and assess prior distributions, and conduct posterior inference using modern computational tools. Core topics include logistic regression for binary outcomes, Poisson and negative binomial models for counts, and model assessment through posterior predictive checks and predictive accuracy criteria (e.g., WAIC, LOO). Hands-on demonstrations in R with the rstanarm and brms packages will illustrate how to implement models, interpret posterior results, and communicate findings effectively. The course also introduces hierarchical extensions for clustered or repeated-measures data, showing how Bayesian GLMs extend naturally to multilevel structures. Emphasis will be placed on best practices for diagnostics, sensitivity analysis, and transparent reporting. Designed for statisticians, data scientists, and applied researchers, the course equips participants with the tools to implement and interpret Bayesian GLMs. Prior exposure to regression modeling and basic Bayesian concepts is recommended but not required.