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 | Professor. Jonty Rougier |

Open unit status | Not open |

Pre-requisites |
MATH21400 Applied Probability 2 and MATH34910 Bayesian Modelling A |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Unit aims

This unit will build 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.

General Description of the Unit

Much of the real advantage of the Bayesian approach to statistical modelling and inference, as compared to classical approach, 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 (for example, mortality statistics in different hospitals, or growth data in different children), and where the parameters describing the groups can be assumed to be similar - that is, not identical but not completely unrelated either.

To keep track of the different kinds of variation in these situations (for example, uncertainty in overall mortality, variation between hospitals, and variation among patients), it is useful to lay out the variables in a diagram, and the unit will include an introduction to these 'graphical models'.

We will go on to discuss how to draw inference in such models (answer - by Bayes' theorem!), and then how to actually do that in practice, since we will no longer have conjugacy to help us, as in Bayesian Modelling A. This leads 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 a range of interesting examples.

Relation to Other Units

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).

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

Learning Objectives

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.

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

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.

The following texts may be useful for reference:

- Bernardo, J.M. and Smith, A.F.M. Bayesian Theory, John Wiley and Sons.
- Gamerman, D. Markov Chain Monte Carlo, Chapman and Hall.
- Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, 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.
- Robert, C.P. The Bayesian Choice, Springer-Verlag.
- Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.