Bayesian Regression: Theory & Practice


Michael Franke

This site provides material for an intermediate level course on Bayesian linear regression modeling. The course presupposes some prior exposure to statistics and some acquaintance with R.

Intended audience

This course is designed for people who have completed a first, introductory course on data analysis, which has conveyed roughly the following:

  • basic knowledge of R and, ideally, the tidyverse
  • basic familiarity with Bayesian reasoning (prior, likelihood, posterior)
  • some prior exposure to regression modeling (Bayesian or otherwise)


The aim of this course is to increase students overview over topics relevant for intermediate to advanced Bayesian regression modeling. The course focuses on Bayesian multi-level generalized linear models as implemented in the brms package. It covers, among other things, the following theoretical and practical aspects:

  • prior and posterior model checking
  • generalized linear models (ordered logit, multinomial, Poisson, Beta …)
  • MCMC methods (HMC diagnostics)
  • distributional and non-linear models (GAMs, Gaussian processes)
  • model comparison (Bayes factors, cross-validation)

Additional material

An even more basic introduction to data analysis (introducing R, tidyverse, Bayesian and, eventually, also frequentist statistics) is the webbook “An introduction to Data Analysis”. This course presupposes roughly the content covered in Chapters 2–9 and 12–13.


Part of the hands-on material (wrangling, plotting, simple regression modeling) was used in a previous course, co-taught with the great Timo Roettger. My gratitude for his permission to build on it here. The tutorial on contrast coding was first authored by Polina Tsvilodub.