# ST301: Bayesian Statistics

###### Lecturer(s): Dr Ric Crossman

*Important: If you decide to take ST301 you cannot then take ST413. Bear this in mind when planning your module selection. Recall: an integrated Masters student must take at least 120 CATS, of level 4+ modules over their 3 ^{rd} & 4^{th} years.*

*Prerequisite(s)**:* Either ST218/219 Mathematical Statistics A&B or ST220 Introduction to Mathematical Statistics

* Commitment:* 3 lectures per week and one tutorial each in weeks 3, 7, and 9.This module runs in Term 1.

*Content**:* Bayesian statistics is one of the fastest growing areas in statistics. With the advance of computer technology it is now a highly practical methodology for addressing many important high dimensional decision problems as well as being underpinned by a sound mathematical foundation. It is especially useful when some of the components of uncertainty have only sparsely collected data associated with them, so that expert judgements need to be incorporated. The course first introduces the central concepts of Bayesian decision analysis through a selection of simple examples. Various methodologies are then presented for:

- Structuring a decision problem – for example by decision trees and influence diagrams.
- Eliciting probability distributions over many variables – using the concepts of irrelevance and the Belief net.
- Eliciting the objectives and preferences of the client – developing the ideas of m.u.i.a. and value independence and the use of the decision conference.

The formal methodologies are illustrated through a wide range of examples for health, the environment, finance and public sector administration. Some of the examples build on the practical experience of the module’s original creator as an active Bayesian decision analyst.

** Aims**:

- To demonstrate how to build statistical models of non-trivial problems when data is sparse and expert judgements need to be incorporated.
- To give ways to represent the pertinent features of a decision problem.
- To give practical algorithms for finding decision rules which the client can expect will best satisfy pre-specified objectives.
- To train the student in the rudiments of decision analysis.

** Objectives**:

- The student will gain an appreciation of the importance of conditional independence in subjective (Bayesian) statistical modelling and be introduced to the DAG as an efficient representation of collections of conditional independence statements as they arise in practice.
- The student will be provided with techniques for eliciting subjective probability distributions over many variables.
- The student will be provided with techniques for eliciting quantitative preference structures from a client which may involve competing objectives.
- The student will obtain an appreciation of the foundational arguments that justify expected utility maximisation as a paradigm for rational action.
- The student will obtain practice in implementing these techniques.
- The student will learn the bases of fast algorithms for the calculation of probabilities needed in such maximisation.

*Assessment**: * 100% by 2-hour examination.