Unit name | Bayesian Modelling |
---|---|
Unit code | MATH30015 |
Credit points | 20 |
Level of study | H/6 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Dr. Gerber |
Open unit status | Not open |
Pre-requisites | |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Bayesian statistics is an area that has grown rapidly in popularity over the past 20 years or so largely as a result of computational advances which have made the approach far more applicable. In this unit we will discuss the Bayesian approach to statistical analysis and modelling. We introduce the basic elements of Bayesian theory, beginning with Bayes theorem, and go on to discuss the applications of this approach to statistical modelling. Topics discussed will include the construction of prior and posterior distributions and hierarchical models, large sample inference and connections to non-Bayesian methods, model checking, and a brief introduction to the computational tools which make analysis possible (in particular Markov chain Monte Carlo methods).
Much of the real advantage of the Bayesian approach to statistical modelling and inference, as compared to classical approach, is only seen when dealing with slightly more complex situations. Hierarchical models allow us to model situations where we simultaneously analyse different groups of data (for example, mortality statistics in different hospitals, or growth data in different children), and where the parameters describing the groups can be assumed to be similar but not identical.
We will study how to formulate and use such models (answer - by Bayes's theorem!), and then how to actually do that in practice, since we will no longer have conjugacy to help us, as in the first part of this unit. This leads to discussion of Markov chain Monte Carlo (MCMC) techniques, which are powerful and elegant algorithms based on simple ideas of conditional probability. Hierarchical models and MCMC come together in the JAGS software, which can be run within R. We will use JAGS to analyse several famous problems, and also some new ones.
The students will be able to:
Lectures (theory and practical problems) supported by handouts and worksheets, some of which involve computer practical work with R and JAGS. A weekly Office Hour. Regular formative problem sheets.
20% computing assessment, 80% examination (2.5 hours)
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
Recommended:
Further: