Bayesian Methodology in Biostatistics

Course material for BST 249

Instructor: Jeff Miller
Spring 2021
Harvard T.H. Chan School of Public Health
Department of Biostatistics

Synopsis

This course covers the essential models, inference techniques, and basic theory of Bayesian analysis. We cover classic models such as mixtures, GLMs, and HMMs, as well as admixtures, Dirichlet processes, and Gaussian processes. In addition to standard MCMC techniques, we look at slice sampling, Hamiltonian Monte Carlo, and variational inference. Recent techniques for scaling to big data are also covered. Case studies are used to connect the concepts to real applications in the literature.

General information

Syllabus
Textbooks:

Bayesian Data Analysis (Third Edition), by Gelman, Carlin, Stern, Dunson, Vehtari, and Rubin. Chapman & Hall/CRC Press, 2013. (REQUIRED)
Pattern Recognition and Machine Learning, by Christopher Bishop. Springer Science+Business Media, 2006. (RECOMMENDED)

Lecture notes

1. Introduction
2. Foundations
3. Conjugate priors
4. Gaussian models
5. Bayesian linear regression
6. Monte Carlo
7. Gibbs sampling
8. Markov chain Monte Carlo
9. Finite mixture models
10. Dirichlet process models
11. Admixture models
12. Variational inference and LDA
13. Automatic variational inference
14. Hidden Markov models
15. Gaussian processes
16. Variable selection
17. Advanced Monte Carlo
18. Hamiltonian Monte Carlo and NUTS
19. Scaling to big data
20. Model building and criticism