The aim of the unit is to provide a thorough introduction to the Bayesian approach to statistical analysis and modelling as well as an introduction to the computational tools that make the use of Bayesian methods possible in practice.
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 first discuss the Bayesian approach to statistical analysis. Topics discussed will include the construction of prior and posterior distributions, Bayesian decision theory, Bayesian asymptotics and model choice. We will then provide a brief introduction to Markov chain Monte Carlo methods which make Bayesian analysis possible in practice. The last part of unit is devoted to the Bayesian approach to statistical modelling, with emphasis on hierarchical models.
Relation to other units
The Theory of Markov chain Monte Carlo methods is covered in more detail in Monte Carlo Methods.
After taking this unit, students will:
- Understand the principles and the theory underlying Bayesian statistics.
- Be able to understand and use Markov chain Monte Carlo methods in order to apply Bayesian methods in practice.
- Be able to build and represent complex models using Bayesian networks.
Reading and References
- Robert, C.P, The Bayesian Choice, 2nd ed., Springer-Verlag, 2007
- J. M. Bernardo and A. Smith. Bayesian Theory, Wiley.
- J.-M. Marin and C. P. Robert. Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer-Verlag.
- 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.
- Gilks, W.R., Richardson, S. and Spiegelhalter, D. Markov Chain Monte Carlo in Practice, Chapman and Hall.
- Morgan, B.J.T. Elements of Simulation, Chapman and Hall.
Unit code: MATH30015
Level of study: H/6
Credit points: 20
Teaching block (weeks): 2 (13-24)
Lecturer: Dr Mathieu Gerber
Statistics 2 (MATH20800), Probability 2 (MATH20008)
Methods of teaching
Lectures supported by lecture notes. A weekly Office Hour. Regular formative problem sheets.
Methods of Assessment
The pass mark for this unit is 40.
The final mark is calculated as follows:
- 20% Computing Assessment
- 80% 2 hours 30 minutes Examination in May/June
NOTE: Calculators of an approved type (non-programmable, no text facility) are allowed.
For information resit arrangements, please see the re-sit page on the intranet.
Further exam information can be found on the Maths Intranet.