Bayesian Statistics
Autumn semester 2019
General information
Lecturer  Dr. Fabio Sigrist 

Lectures  Tue 1517 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 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  Noninformative 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, MetropolisHastings 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).