Unit information: Bayesian Modelling B in 2013/14

Unit name	Bayesian Modelling B
Unit code	MATH34920
Credit points	10
Level of study	H/6
Teaching block(s)	Teaching Block 2C (weeks 13 - 18)
Unit director	Dr. Yu
Open unit status	Not open
Pre-requisites	MATH34910, MATH21400
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

This unit will develop on the material covered in Bayesian Modelling A, and will provide the necessary background, experience and modern computational tools to apply Bayesian modelling techniques to realistic applications. The course will start with a gentle introduction to the basic principles of Monte Carlo techniques, with examples of applications in science. The elegance, simplicity and power of the concepts will motivate their use in the context of Bayesian inference. The course will then focus on Markov Chain Monte Carlo and Sequential Monte Carlo techniques. These methods have revolutionised statistical inference over the last 10 - 15 years. The application of these powerful tools will be gradually introduced and illustrated with practical examples from various fields of science, including finance, telecommunications, biology, and nuclear science.

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

This unit is currently also available at Level 7. However 2011/12 is the last year in which this option is available. From 2012/13 the unit will only be available at Level 6.

The Level 7 units that build on the methods and knowledge discovered in Bayesian Modelling B are Monte Carlo Methods (M6001) and Graphical Modelling (M6002).

Intended Learning Outcomes

The students will be able to:

• Represent complex data by means of a hierarchical model

• Display such a model graphically

• Understand and apply MCMC techniques for performing Bayesian analysis in practice

• Justify theoretically the use of the various algorithms encountered.

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.

Assessment Information

The assessment mark for Bayesian Modelling B is calculated from a 1½-hour written examination in May/June consisting 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.
2. Gamerman, D. Markov Chain Monte Carlo, Chapman and Hall.
3. Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, Chapman and Hall.
4. Gilks, W.R., Richardson, S. and Spiegelhalter, D. Markov Chain Monte Carlo in Practice, Chapman and Hall.
5. Morgan, B.J.T. Elements of Simulation, Chapman and Hall.
6. Robert, C.P. The Bayesian Choice, Springer-Verlag.
7. Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.