STAT 520A - Bayesian analysis

Description

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.

Key links

• Detailed syllabus

• Recordings (Canvas > Files > Recordings)

• Piazza

• Last year's course (template for this year, if you want to peek full set of topics covered)

Schedule

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 Regression	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 Mixtures	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