# Bayesian Statistics

Autumn semester 2017

## General information

Lecturer Dr. Fabio Sigrist Tue 15-17 HG D 3.2 >> >>

## 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

• August 25th 2017:
Beginning of lecture: Tuesday, 19/09/2017.

## Course materials

• Organization sheet
• Lecture Notes

Week Date Topic
1 19/09 Interpretations of probability, Bayes formula, basics of Bayesian statistics
2 26/09 Point estimation and decision theory, testing, Bayes factor
3 03/10 Credible sets, Bayesian asymptotics, likelihood principle
4 10/10 Conjugate priors, Jeffreys prior and examples
5 17/10 Reference prior, expert priors, priors as regularizers
6 24/10 Hierarchical Bayes models and examples
7 31/10 Empirical Bayes and examples
8 07/11 Bayesian linear regression model and model selection
9 14/11 Laplace approximation, independent Monte Carlo methods
10 21/11 Rejection sampling, importance sampling, Basics of Markov chain Monte Carlo
11 28/11 MCMC, Gibbs sampler, Metropolis-Hastings algorithm
12 05/12 Adaptive MCMC, Hamiltonian Monte Carlo
13 12/12 Sequential Monte Carlo, approximate Bayesian computation
14 19/12 reserve / buffer

## 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.

Date Topic Exercises Solutions Due date
26/09 Posterior predictive distribution, Bayesian decision theory, Bayesian testing, Bayes factor Series 1 Solution 03/10
10/10 Credible intervals, conjugate priors, improper priors Series 2 Solution 17/10
24/10 Jeffreys prior and expert priors Series 3 Solution 31/10
07/11 Empirical Bayes, Bayesian regression model Series 4 Solution 14/11
28/11 MCMC: Gibbs sampler, random walk Metropolis algorithm Series 5 Solution 05/12
12/12 Hamiltonian Monte Carlo Series 6 Solution 19/12

## Literature

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