# Bayesian Statistics

Course category:
3rd year
Module code:
0530001
Year:
2010/11
Term:
Spring
Credits:
10
Lecturer:
Dr Peter Lee

## Aims

The aim of the module is to introduce the basic notions of Bayesian statistics, showing how Bayes Theorem provides a natural way of combining prior information with experimental data to arrive at a posterior probability distribution over parameters and to show the differences between classical (sampling theory) statistics and Bayesian statistics.

## Learning objectives

At the end of the module you should be able:

• To understand the basic notions of Bayesian statistics;
• To prove and use Bayes Theorem in its various forms;
• To carry out an analysis of normally distributed data with a normal prior distribution;
• To be able to carry out a significance test of a point (or sharp) null hypothesis using a full Bayesian methodology;
• To understand the differences between classical statistics and Bayesian statistics.

## Syllabus

• Introduction and binomial model
• Bayes theorem with applications, posterior, and nature of posterior
• Conjugate priors
• Bayesian decision theory and point estimation
• Credibility regions, Hypothesis testing
• Normal mean model, normal variance model, and normal mean and variance both unknown
• Reference prior and Jeffreys' rule
• Other models and applications to insurance.

## Recommended texts

• *** P M Lee, Bayesian Statistics: An Introduction, Wiley (SF 4 LEE)
(For most of the material covered, either the second or the third edition will be satisfactory)
.
• ***Andrew Gelman, John B. Carlin, H.S. Stern, and D.B. Rubin, Bayesian Data Analysis, 2nd Edition. Chapman & Hall (SFGEL)
• *** H R Neave, Statistics Tables for mathematicians, engineers, economists and the behavioural and management sciences, London: Routledge (SF 0.83 NEA and REF SF 0.83 NEA).
• * G R Iverson, Bayesian Statistical Inference, Beverley Hills, CA: Sage (SF4 IVE) (for preliminary reading).
• * J Albert, Bayesian Computation with R, Springer 2007 (Not yet in Library) (For computational aspects).
• ** D V Lindley, An Introduction to Probability and Statistics from a Bayesian Viewpoint (2 vols - Part I: Probability and Part II: Inference), Cambridge University Press (S 9 LIN).

## Teaching

• Spring Term
• 2 lectures per week
• 1 problems class per week

## Assessment

One and a half hour closed examination towards the end of the Summer Term 90%,
Coursework 10%. Note that coursework submitted after the advertised deadlines will be given a mark of zero.

## Elective information

A course on Bayesian statistics showing how to make inferences by combining prior beliefs with information obtained from experimental data.

Please check prerequisites carefully before asking to take this module as an elective.