# Bayesian Statistics

Autumn semester 2019

## General information

Lecturer Dr. Fabio Sigrist Tue 15-17 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 1st 2019:
Beginning of lecture: Tuesday, 17/09/2019.

## Course materials

Week Date Topic
1 17/09 Introduction, Bayes formula, basics of Bayesian statistics, interpretations of probability
2 24/09 Point estimation and decision theory, testing, Bayes factor
3 01/10 Credible sets, Bayesian asymptotics, likelihood principle, conjugate priors
4 08/10 Non-informative priors, improper priors, Jeffreys prior
5 15/10 Reference prior, expert priors, priors as regularizers
6 22/10 Hierarchical Bayes models
7 29/10 Empirical Bayes
8 05/11 Bayesian linear regression model & model selection
9 12/11 Laplace approximation, independent Monte Carlo methods
10 19/11 Rejection sampling, importance sampling, Basics of Markov chain Monte Carlo
11 26/11 MCMC, Gibbs sampler, Metropolis-Hastings algorithm
12 03/12 Adaptive MCMC, Hamiltonian Monte Carlo
13 10/12 Sequential Monte Carlo, approximate Bayesian computation
14 17/12

## Series and solutions

Submitting solutions to the exercise is not compulsory except for some PhD students. You can hand in your solution in the corresponding tray in HG J68 or by email to Marco Eigenmann.

Date Topic Exercises Solutions Due date
24/09 Posterior predictive distribution, Bayesian decision theory, Bayesian testing, Bayes factor
08/10 Credible intervals, conjugate priors, improper priors
22/10 Jeffreys prior, reference prior, expert priors
05/11 Empirical Bayes, Bayesian regression model
26/11 MCMC: Gibbs sampler, random walk Metropolis algorithm
10/12 Hamiltonian Monte Carlo

## Literature

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