Bayesian Analysis


Bayesian analysis is revolutionary. It can estimate complex models that have no analytical solutions and also incorporate prior knowledge. This course introduces Bayesian analysis in a conceptually accessible way, with a focus on application and interpretation. Selected topics include the history of Bayesian analysis, the Bayes theorem, the basics of likelihood theory, the Markov chain Monte Carlo methods, applications of the Bayesian methods for estimating generalized linear models and multilevel regression models, and post-estimation analysis (model diagnostics and comparisons). Examples and R code will be provided. Knowledge of R and linear regression is required. 

Agenda (Request syllabus)

Day 1: Bayesian Framework and Bayesian Linear Regression

Day 2: Bayesian Estimation and Bayesian Generalized Linear Models

Day 3: Bayesian Inference and Multilevel Regression Models


Dr. Jun Xu is Professor of Sociology and Data Science at Ball State University. He received a Ph.D. in Sociology from Indiana University (Bloomington) and has been teaching methods courses for over 15 years. His methodological interests include Bayesian statistics, categorical data analysis, causal inference, machine learning, etc. He is the author of Modern Applied Regressions: Bayesian and Frequentist Analysis of Categorical and Limited Response Variables with R and Stan (Chapman & Hall/CRC) and a co-author of Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives (with Andrew S. Fullerton, Chapman & Hall/CRC). He has published in Sociological Methods and Research, Social Science Research, and The Stata Journal and has authored or co-authored several statistical application packages, including "gencrm", "grcompare", and the very popular "SPost 9.0" package in Stata and "stdcoef" in R.

Class Time

June 26-28 (11am-1:30pm, US ET), 2024  and on-demand. Lecture and lab materials and recordings are available to view at your convenience.


Participants were from CDC, Georgia State University, Hebrew University of Jerusalem, Sun Yat-sen University, Syracuse University, University of Pittsburg, etc. Below are sampled reviews from past participants.

This is a great class and cleared up so many confusions and misunderstandings I had previously about both Bayesian and Frequentist statistics. This course is great for those who have quantitative skills to learn Bayesian analysis while reviewing the Frequentist statistics. It is also wonderful for the beginners to understand the basics of Bayesian analysis. Of course, the most wonderful part is the lab session which provides detailed R codes about how to run and interpret Bayesian models. 

Dr. Xu provides very thorough and helpful details in the lectures and lab guides. I found them invaluable.

Great introduction to Bayesian statistics (compared to frequentist statistics). The slides and exercises were complementary!

I like the most about the labs and hands on examples and the instructor's comments on p values and model complexity.

I really like the way that the class was organized and that it was interactive.