Unit information: Bayesian Modelling B 34 in 2012/13

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

Description including Unit Aims

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.

Intended Learning Outcomes

The students will be able to:

1. Represent complex data by means of a hierarchical model
2. Display such a model graphically
3. Understand and apply MCMC techniques for performing Bayesian analysis in practice
4. Justify theoretically the use of the various algorithms encountered
5. Use software programs to implement algorithsm covered in this unit

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.

Teaching Information

Lectures, (theory and practical problems) supported by example sheets, some of which involve computer practical work with R and WinBugs, and a mini-project.

Assessment Information

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.

Reading and References

The following texts may be useful for reference:

1. Bernardo, J.M. and Smith, A.F.M. Bayesian Theory, John Wiley and Sons. #Gamerman, D. Markov Chain Monte Carlo, Chapman and Hall.
2. Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, Chapman and Hall.
3. Gilks, W.R., Richardson, S. and Spiegelhalter, D. Markov Chain Monte Carlo in Practice, Chapman and Hall.
4. Morgan, B.J.T. Elements of Simulation, Chapman and Hall.
5. Robert, C.P. The Bayesian Choice, Springer-Verlag.
6. Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.