Computational statistics, spring 2012

Lecturer

Petri Koistinen

Scope

8 cu.

Type

Advanced studies

Prerequisites

Basic probability theory (some familiarity of working with more than one random variables is assumed). Basic knowledge about vector and matrix operations. Some exposure to Bayesian inference would be beneficial. Some experience in computer programming would also be helpful.

Lectures

Periods III and IV, Monday 10-12 and Wednesday 12-14, room B120.

Easter holiday 5.-11.4.

News

Change of schedule: in period IV, exercise sessions are held in room B321 on Wednesdays at 14-16 (after the lecture).

See the CompStat moodle page.

Go to HY-Moodle, log in with your University of Helsinki (AD) user name and password, and register to the course Computational Statistics (if you haven't done that already); the course key is compstat12.

Exams

Two course exams at the end of each of the periods III and IV. Alternatively, a separate exam.

General advice for the two course exams: You should bring a pencil and an eraser. You will be provided blank paper. Additionally, you are allowed to (but need not) bring a calculator and a lightweight (less than half a kilogram) book of mathmetatical tables/formulas (for Finns: MAOL taulukot).

First course exam is held in room B120 on Wednesday 29 February at 12-14. Area of the exam is Chapters 1-5 of the lecture notes (skip Sections 3.3.2, 4.5.3 and 4.6.3 as well as the discussion of a confidence interval for a ratio of expectations in Section 4.2) and exercise sessions 1-5.

Second course exam is held in room B120 on Wednesday 9 May at 12-14. Area of the exam consists of exercise sessions 6-10 and Chapters 6-10 of the lectures notes (skip Sections 6.4, 7.4.6, 8.5 and 10.7).

Description

This course gives an overview of computational methods which are useful especially in Bayesian statistics (but some of the methods are also used widely in frequentist inference)

• Review of probability and Bayesian inference.
• Methods for generating independent samples from distributions.
• Classical Monte Carlo integration and importance sampling.
• Approximating the posterior distribution using numerical quadrature or Laplace expansion.
• MCMC methods: Gibbs and Metropolis-Hastings sampling.
• Auxiliary variable methods in MCMC.
• EM algorithm.
• Multi-model inference.
• MCMC theory.

There will be several examples in the lectures and in the exercise sessions which show how the methods can be implemented using the R system for statistical computing. R is convenient for us since it is freely available and widely used and it enables easy visualization of results and contains simulation functions for lots of distributions. However, the methods are in no way tied to the R environment, and the methods can as easily be used in many other environments (such as Matlab together with its Statistics toolbox).

Lecture notes

• Part 1: Chapters 1-5 and Appendices A and B.
• Part 2: Chapters 6-11.

Practical work

In order to get the credits, you need to pass also the compulsory practical work (harjoitustyö). It would be ideal to do the work in groups of two or three. More information later.

Useful links

• Wikipedia's List of probability distributions is a treasure trove of information on familiar distributions. NB: Wikipedia's parametrization differs in some cases from the parametrization used in the lecture notes.
• Wikipedia: English pronunciation of Greek letters.
• R: R project homepage; download R from CRAN.
• BUGS: OpenBUGS, WinBUGS.
• JAGS, Just Another Gibbs Sampler, a system not wholly unlike BUGS.

Registration

Did you forget to register? What to do.

Exercise groups

No exercises on the first week of period III or period IV.

You will get additional points from solving the exercises, which will be added to your points from the two course exams.

The exercise material is available on the moodle page of the course. Go to HY-Moodle, select the course Computational Statistics, log in with your University of Helsinki (AD) user name and password, and register to the course moodle page; the course key is compstat12.