Unit information: Bayesian Modelling A in 2013/14

Unit name	Bayesian Modelling A
Unit code	MATH34910
Credit points	10
Level of study	H/6
Teaching block(s)	Teaching Block 1B (weeks 7 - 12)
Unit director	Dr. Tadic
Open unit status	Not open
Pre-requisites	MATH20800
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

This unit will introduce you to an alternative approach to statistical modelling and inference, with a rather different flavour from those taught elsewhere in our programmes. The main aims of the unit are to acquaint you with the basic concepts of Bayesian statistics, and to provide you with the necessary background and experience to apply Bayesian modelling techniques to realistic statistical problems. This unit will discuss 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.

Aims

This unit will introduce you to an alternative approach to statistical modelling and inference, with a rather different flavour from those taught elsewhere in our programmes. The main aims of the unit are to acquaint you with the basic concepts of Bayesian statistics, and to provide you with the necessary background and experience to apply Bayesian modelling techniques to realistic statistical problems.

Syllabus

Bayesian Statistics: Bayes theorem; prior and posterior distributions; prior specification and conjugacy; large sample properties; Bayes estimates and credible intervals.

Statistical Modelling: Hierarchical models, model checking.

Monte Carlo Methods: Gibbs sampling for hierarchical Bayes models.

Intended Learning Outcomes

The students will be able to:

• Understand and explain the theoretical basis for and range of applications of the Bayesian approach to statistical modelling;

• Describe and construct realistic and appropriate statistical models to describe a wide variety of modelling situations;

• Use and understand appropriate computational methodology within a Bayesian framework.

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 Matlab as a programmable statistical package, interpretation of computational results, time-management, independent thought and learning, and written communication.

Teaching Information

Lectures, supported by example sheets.

Assessment Information

The assessment mark for Bayesian Modelling A is calculated from a 1½-hour written examination in April consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed.

Reading and References

• Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, Chapman and Hall.

• J.-M. Marin and C. P. Robert. Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer-Verlag.

• Robert, C.P. The Bayesian Choice, Springer-Verlag.

• J. M. Bernardo and A. Smith. Bayesian Theory, Wiley.

• Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.

• D. Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman and Hall.