Unit name | Bayesian Modelling B 34 |
---|---|
Unit code | MATHM4920 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Dr. Yu |
Open unit status | Not open |
Pre-requisites |
Applied Probability 2 (MATH 21400), Bayesian Modelling A (MATH 34910) |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Much of the real advantage of the Bayesian approach to statistical modelling and inference is only seen when dealing with the slightly more complex situations encountered in this unit. Hierarchical models allow us to model situations where we simultaneously analyse different groups of data and where the parameters describing the groups can be assumed to be similar, using 'graphical keep track of the different kinds of variation. We will discuss how to draw inference in such models, and then how to actually do that in practice, leading to discussion of Markov chain Monte Carlo (MCMC) techniques, which are powerful and elegant algorithms based on simple ideas of conditional probability. Graphical modelling and MCMC are the basis for a package called WinBugs for doing Bayesian analysis without needing to write your own program, and there will be demonstrations and some hands-on practice with using that package on range of interesting examples.
Aims
This unit will develop on the material covered in Bayesian Modelling A, both by extending the range of models considered to include hierarchical specifications, and by deriving probabilistic algorithms that enable the practical use of Bayesian methods in a very broad range of applications.
Syllabus
Hierarchical models; Directed acyclic graphs; Markov chain Monte Carlo; Gibbs sampler; Metropolis-Hastings algorithm; Application to analysing data, and posterior summaries.
Relation to Other Units
The unit is based on the same lectures as Bayesian Modeling B (MATH 34920), and has the same lectures and examinations as that unit. Students taking this unit, however, will be required to complete a mini-project that will be assessed as 20% of the final mark.
The students will be able to:
Transferable Skills:
In addition to the general skills associated with other mathematical units, you will also have the opportunity to gain practice in the following: computer literacy and general IT skills, use of R and WinBugs as programmable statistical packages, interpretation of computational results, time-management, independent thought and learning, and written communication.
Lectures, (theory and practical problems) supported by example sheets, some of which involve computer practical work with R and WinBugs, and a mini-project.
The assessment mark for Bayesian Modelling B is calculated from a 1½-hour written examination in May/June (80%) and a mini-project (20%). The written examination will consist of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are NOT permitted to be used in this examination.
The following texts may be useful for reference: