MAT-51706 Bayesian methods, periods 3-4 (2006-2007), 6 credits
MAT-51700 Bayesin menetelmät

Introduction

Bayesian methods allow statistical analysis combining measured data and a priori information.

Period 3: theoretical background for understanding Bayes formula and its use in statistical analysis. Introduction to random variables and conditional expectations..

Period 4: practical skills for computerized Bayesian analysis using Monte Carlo Markov chain methods is given using Matlab.

Information on the lecturer´s research interests can be found here.

Lectures

Lecturer: professor Samuli Siltanen. The following times and places are used: Wednesday 10-12 (SJ208), Wednesday 14-16 (SJ202) and Thursday 10-12 (SJ208). Each week may be different and consist of a combination of lectures, exercise sessions or presentations by students. Please follow the weekly schedule below.

Lectures are given in Finnish or English depending on the audience.

Lecturer´s office hour Thursday 13-14 (room TD 321).

How to pass the course?

The following two are required:
1. Presentation about a given topic. (See below.)
2. Successful completion of a given Matlab project work.

Presentations

Time for each presentation is 45 minutes. Please condense the material or leave parts out so that the presentation does not become too long. Chapters below refer to the book by Shiryayev.

Wednesday 24.1.2007
10-11 Chapter II§1, Sami Tiainen
11-12 Chapter II§2 (Borel sets), Matti Saarela
14-15 Chapter II§3 (Shorten!), Emilia Ylirinne
15-16 Chapter II§4, Christian Rapold

Thursday 25.1.2007
10-11 Chapter II§7 (until 7 on page 225), Gernot Härzel
11-12 Chapter II§7 (remaining part), Henri Pesonen

Wednesday 28.2.
10-11 Jussi-Pekka Penttinen (Ergodic Theorem)
11-12 Timo Pylvänäinen (Theory of Markov chains)

Project works

Topics for the project works will be discussed and assigned in the beginning of Period 4. Suggestions for topics are welcome from the students as well.

There will be a set of lectures (including one presentation by a student) about Markov chain Monte Carlo (MCMC) methods, that will be useful in the project works.

In the remaining lecture time slots the lecturer is available for discussions about the project works. Please agree on meeting times beforehand by email.

Schedule:
Wednesday February 7 10-12: assignment of project work topics.
Thursday February 8 10-12: Lecture on MCMC methods
Wednesday February 14 10-11: Lighthouse (Matti, Henri, Emilia, Sami)
Wednesday February 14 11-12: Rounded data (Jussi-Pekka)
Thursday February 15 10-11: Coarse data (Gernot, Christian)
Thursday February 15 11-12: Analysis of Proportions (Timo)
Wednesday March 7 10-11: Lighthouse group meeting

Course material

Shiryayev: Probability, Springer.
Gelman, Carlin, Stern and Rubin: Bayesian Data Analysis, Chapman & Hall
Tan, Fox and Nicholls: http://www.math.auckland.ac.nz/%7Ephy707/, Chapter 7.

This page was last updated on February 15, 2007.