## MATH3820 Bayesian Statistics

### 10 creditsClass Size: 60

Module manager: Dr Peter Thwaites; Dr Robert Aykroyd
Email: P.A.Thwaites@leeds.ac.uk; R.G.Aykroyd@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2019/20

### Pre-requisite qualifications

MATH2715 or MATH2735.

### This module is mutually exclusive with

 MATH5820M Bayesian Statistics and Causality

This module is not approved as a discovery module

### Module summary

Bayesian statistic methods have had a long and often controversial history; nevertheless, they are widely adopted due to their utility in solving complex inference problems. This module introduces the Bayesian approach to statistical inference and decision making. The module covers both philosophical and computational aspects of adopting a Bayesian approach.

### Objectives

Bayesian statistics has had a long and often controversial history. It gives us a rigorous framework in which to combine prior beliefs and expectations with observed data from many sources – a process that we all do informally. This framework also opens up many opportunities for analyses of complex problems that cannot be adequately handled using traditional statistical techniques. The objective of this module is to introduce Bayesian statistical methods through the consideration of philosophical differences with traditional statistical procedures and the application of Bayesian techniques. This module also introduces the ideas of quantitative decision theory and rational decision making.

Learning outcomes
On completion of this module, students should be able to:
(a) discuss the differences between Bayesian and traditional statistical methods;
(b) derive prior, posterior and predictive distributions for standard Bayesian models;
(c) tackle hierarchical analyses using sampling methods;
(d) produce network representations of joint distributions and perform updates on small networks;
(e) define utility in the context of decision making and apply decision analysis methods to simple finite dimensional problems;
(f) use a statistical package with real data to facilitate an appropriate analysis and write a report interpreting the results.

### Syllabus

1. Degrees of belief and subjective probabilities,
2. The likelihood (choice, exchangeability and the likelihood principle),
3. Prior, posterior and predictive distributions in conjugate analyses,
4. Specification of prior distributions through elicitation and principles of ignorance,
5. Modelling complex problems with potentially disparate data sources using hierarchical techniques,
6. Bayesian updating using sampling techniques including prior-sample reweighting and Gibbs sampling,
7. Network representations of joint probability distributions and their use in Bayesian updating,
8. Quantitative decision analysis: minimax decisions through to utility theory.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Practical 1 2.00 2.00 Private study hours 76.00 Total Contact hours 24.00 Total hours (100hr per 10 credits) 100.00

### Private study

Reviewing lecture notes and wider reading: 31 hours;
Completing exercise sheets: 20 hours;
Completing assessed practical: 20 hours.

### Opportunities for Formative Feedback

Exercise sheets provided throughout the semester covering various topics.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Practical Report on an applied Bayesian Analysis 20.00 Total percentage (Assessment Coursework) 20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated