STAT 520A - Bayesian analysis

Bayesian statistics provides a wide range of tools to approach data analysis. This course is composed of (1) a Bayesian "bootcamp" facilitated by probabilistic programming languages; (2) more specialized topics, with an emphasis on computational Bayesian statistics; (3) a final project in teams or individually.

Date Topics Due
Tuesday, January 11 Course logistics
What is Bayesian Analysis?
Bayes estimator: a first example
Thursday, January 13 Project guidelines
Bayes estimator: a first example
Point estimates, confidence estimates, and the Bayes estimator
Tuesday, January 18 Point estimates, confidence estimates, and the Bayes estimator
Why Bayes?
Directed graphical models
Readings on decision theoretic foundations
Thursday, January 20 Class cancelled
Optional: exercises on Bayes estimators
Tuesday, January 25 Regression
Hierarchical models
Readings on graphical models
Readings on PPLs
Optional exercises on regression
Thursday, January 27 Basics of model selection
Consistency, misspecification, identifiability
Optional readings on common distributions
Friday, January 28 Calibration
Exchangeability and de Finetti
Consistency, misspecification, identifiability
Optional exercises on hierarchical modelling
Tuesday, February 1 Exchangeability and de Finetti
Calibration, continued; Bernstein-von Mises
Optional exercise (before class)
Readings on goodness-of-fit
Readings on prior distributions
Readings on model selection
Thursday, February 3 Calibration, continued; Bernstein-von Mises
Bayes estimators: properties and optimization
Optional modelling exercise
Friday, February 4 Project proposals
Tuesday, February 8 Class cancelled
Optional readings on exchangeability
Readings on Bayesian clustering
Thursday, February 10 Metropolis-Hastings and slice samplers
Tuesday, February 15 Design of MCMC samplers
Optional readings on slice sampling
Thursday, February 17 Parallel tempering
Approximate Bayesian Computation
Normalization constant estimation via stepping stone
Normalization constant estimation via reversible jumps
Optional Markov chain and linear algebra exercise
Optional global vs. detail balance exercise
Optional exercise on the law of large numbers
Optinal exercise on MCMC on uniforms
Optional exercises on Metropolis-Hastings
Optional MCMC readings
Optional PT readings
Friday, March 18 Final project