Graduate course covering Bayesian inference, prior elicitation, posterior analysis, Bayesian hypothesis testing, hierarchical models, and computational methods such as MCMC and Gibbs sampling.
Intro to Bayesian Inference
Bayes’ Rule
Beta-Binomial Model
Balance and Sequentiality in Bayesian Analyses
Conjugacy and Conjugate Families
Bayes
Prior
Bayesian Model for Normal Data
Approximating the Posterior
MCMC – Simulation and Diagnostics
Model Quality & Bayesian Hypothesis Testing
Bayesian Linear Regression
Bayesian Poisson & Negative Binomial Regression
Bayesian Logistic Regression
Naive Bayes Classification
Hierarchical Models and Pooling
Normal Hierarchical Models
Normal Hierarchical Models with Predictors
Source .tex files are available upon request.
Selected solution files and source code are available upon request.
Project
(This semester I have assigned a project instead of exams)
These materials are provided for practice and illustration purposes only and are not intended to reflect the content or format of future examinations.
Includes code for Bayesian posterior computation, MCMC methods, Gibbs sampling, Metropolis–Hastings algorithms, posterior summaries, and diagnostics.
The R scripts provided here were developed for instructional purposes and reflect working implementations used in this course. While they ran correctly in the instructor’s environment, no guarantee is made regarding correctness, efficiency, or suitability for other settings. Users are encouraged to adapt and validate the code for their own purposes. If you notice any errors, inconsistencies, or opportunities for improvement, I would greatly appreciate being contacted so that corrections can be made.
Probability & Statistics Refresher
Sufficient Statistics
Transformations of Random Variables
Credible vs. Confidence Intervals
Fisher Information and Jeffreys Prior
Markov Chains – Quick Introduction
Markov Chains – Introductory Notes
Markov Chains – Extended Handout
These materials provide supplementary background and conceptual clarification for key topics in Bayesian inference and computation. They are intended to support lectures and assigned readings.
Materials are provided for educational use. While care has been taken in their preparation, errors or omissions may occur. If you notice any errors, inconsistencies, or ambiguities in the lecture notes, homework problems, or sample exams, I would appreciate being contacted so that corrections can be made. Please contact me before reuse or adaptation.