Unit information: Bayesian Modelling A in 2014/15

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. Marcelo Pereyra
Open unit status	Not open
Pre-requisites	MATH20800 Statistics 2
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

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.

General Description of the Unit

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).

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

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

100% Examination

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.

Reading and References

The following texts may be useful for reference:

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