Unit information: Bayesian Modelling in 2020/21

Unit name	Bayesian Modelling
Unit code	MATH30015
Credit points	20
Level of study	H/6
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Dr. Gerber
Open unit status	Not open
Pre-requisites	MATH20800 Statistics 2 and MATH20008 Probability 2
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

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

The Bayesian approach to statistics relies on the idea that probabilities can be used to express our uncertainty about the quantity of interest and that the prior knowledge of the statistician can be updated using conditional probabilities as observations become available. Bayesian statistics 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 in detail 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.

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 Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

80% Timed, open-book examination 20% Coursework: computing assignments

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.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• Christian P. Robert, The Bayesian Choice, 2nd ed., Springer-Verlag, 2007

Further

• Jose M. Bernardo and Adrian F.M. Smith. Bayesian Theory, Wiley, 1994
• Dani Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman and Hall, 2006
• Walter R. Gilks, Sylvia Richardson, and D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice, Chapman and Hall, 1996
• Jean-Michel Marin and Christian P. Robert. Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer-Verlag, 2007
• B.J.T. Morgan, Elements of Simulation, Chapman and Hall, 1984
• Christina P. Robert and George Casella, Monte Carlo Statistical Methods, Springer-Verlag, 2004