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 12 Course logistics
What is Bayesian Analysis?
Bayes estimator: a first example
Thursday, January 14 Project guidelines
Bayes estimator: a first example
Point estimates, confidence estimates, and the Bayes estimator
Tuesday, January 19 Why Bayes?
Directed graphical models
Readings on decision theoretic foundations
Thursday, January 21 Regression
Hierarchical models
Exercises on Bayes estimators
Tuesday, January 26 Hierarchical models
Basics of model selection
Readings on graphical models
Readings on PPLs
Optional readings on common distributions
Thursday, January 28 Calibration
Consistency, misspecification, identifiability
Friday, January 29 Exercises on regression
Exercises on hierarchical modelling
Tuesday, February 2 Calibration
Exchangeability and de Finetti
Optional PT readings
Readings on prior distributions
Readings on model selection
Thursday, February 4 Calibration, continued; Bernstein-von Mises
Short exercise (before class)
Optional modelling exercise
Tuesday, February 9 Bayes estimators: properties and optimization
Readings on goodness-of-fit
Optional readings on exchangeability
Thursday, February 11 Metropolis-Hastings and slice samplers
Project proposals
Tuesday, February 16 No lecture (reading week)
Thursday, February 18 No lecture (reading week)
Tuesday, February 23 Design of MCMC samplers
Parallel tempering
Readings on Bayesian clustering
Optional readings on slice sampling
Optional readings on evaluation of MCMC methods
Thursday, February 25 Approximate Bayesian Computation
Normalization constant estimation via stepping stone
Normalization constant estimation via reversible jumps
Markov chain and linear algebra exercise
Global vs. detail balance exercise
Optional exercise on the law of large numbers
Exercise on MCMC on uniforms
Exercises on Metropolis-Hastings
Tuesday, March 2 MH and slice exercises solutions
Optional MCMC readings
Friday, April 23 Final project