# Unit information: Bayesian Modelling in 2018/19

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Unit name Bayesian Modelling MATH30015 20 H/6 Teaching Block 2 (weeks 13 - 24) Dr. Gerber Not open Statistics 2 (MATH20800), Probability 2 (MATH20008) None School of Mathematics Faculty of Science

## Description

Unit aims

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.

Unit description

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.

## Intended learning outcomes

After taking this unit, students will:

1. Understand the principles and the theory underlying Bayesian statistics.
2. Be able to understand and use Markov chain Monte Carlo methods in order to apply Bayesian methods in practice.
3. Be able to build and represent complex models using Bayesian networks.

## Teaching details

Lectures (theory and practical problems) supported by handouts and worksheets, some of which involve computer practical work with R and JAGS. A weekly Office Hour. Regular formative problem sheets.

## Assessment Details

20% computing assessment, 80% examination (2.5 hours)

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.

Recommended:

1. Robert, C.P, The Bayesian Choice, 2nd ed., Springer-Verlag, 2007

Further:

1. J. M. Bernardo and A. Smith. Bayesian Theory, Wiley.
2. J.-M. Marin and C. P. Robert. Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer-Verlag.
3. Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.
4. D. Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman and Hall.
5. Gilks, W.R., Richardson, S. and Spiegelhalter, D. Markov Chain Monte Carlo in Practice, Chapman and Hall.
6. Morgan, B.J.T. Elements of Simulation, Chapman and Hall.