Bayesian Statistics
Autumn semester 2021
General information
Lecturer  Dr. Fabio Sigrist 

Lectures  Tue 1618 HG G 3 >> 
Course catalogue data  >> 
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  Noninformative 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, MetropolisHastings 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).