# Bayesian Statistics

Autumn semester 2021

## General information

Lecturer Dr. Fabio Sigrist Tue 16-18 HG G 3 >> >>

## Course content

Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.

## Announcements

• September 3rd 2021:
Beginning of lecture: Tuesday, 21/09/2021.

All the course materials can be found on the Moodle webpage. An overview is given below.
Week Date Topic
1 21/09 Introduction, Bayes formula, basics of Bayesian statistics, interpretations of probability
2 28/09 Point estimation and decision theory, testing, Bayes factor
3 05/10 Credible sets, Bayesian asymptotics, likelihood principle, conjugate priors
4 12/10 Non-informative priors, improper priors, Jeffreys prior
5 19/10 Reference prior, expert priors, priors as regularizers
6 26/10 Hierarchical Bayes models
7 02/11 Empirical Bayes
8 09/11 Bayesian linear regression model & model selection
9 16/11 Laplace approximation, independent Monte Carlo methods
10 23/11 Rejection sampling, importance sampling, Basics of Markov chain Monte Carlo
11 30/11 MCMC, Gibbs sampler, Metropolis-Hastings algorithm
12 07/12 Adaptive MCMC, Hamiltonian Monte Carlo
13 14/12 Sequential Monte Carlo, approximate Bayesian computation
14 21/12

## Series and solutions

Submitting solutions to the exercises is not compulsory except for some PhD students. You can hand in your solutions by email to Drago Plecko.

Date Topic Exercises Solutions Due date
28/09 Posterior predictive distribution, Bayesian decision theory, Bayesian testing, Bayes factor Series 1 Solutions 1 05/10
12/10 Credible intervals, conjugate priors, improper priors Series 2 Solution 2 19/10
26/10 Jeffreys prior, reference prior, expert priors Series 3 Solution 3 02/11
09/11 Empirical Bayes, Bayesian regression model Series 4 Solution 4 16/11
30/11 MCMC: Gibbs sampler, random walk Metropolis algorithm Series 5 Solution 5 07/12
14/12 Hamiltonian Monte Carlo Series 6 Solution 6 21/12

## Literature

• Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007.
• A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013).