Module Catalogue 2026/27

Pre Requisite Comment

MAS2907, Stochastic Processes, is useful but not essential.

Co Requisite Comment

N/A

Aims

To gain an understanding of the principles of Bayesian statistics and practical applications of more complex models relevant to practical data analysis. To be introduced to the principles of Bayesian decision theory.

Outline Of Syllabus

Review of Bayesian inference for singular parameter models. Inference for multi-parameter models using conjugate prior distributions: mean and variance of a normal random sample. Introduction to Markov chain Monte Carlo methods: Gibbs sampling, Metropolis-Hastings sampling, mixing and convergence. Application to regression modelling such as linear models, generalised linear models and extensions. Computation using R. Principles of Bayesian decision theory.

Intended Knowledge Outcomes

At the end of the module, it is expected that a student will be able to:
- Describe how to make inferences for multi-parameter models using Bayesian approach.
- Describe the use of Markov chain Monte Carlo methods for inference.
- Define the key elements of Bayesian decision theory.

Intended Skill Outcomes

At the end of the module it is expected that a student will be able to:
- Apply the Bayesian approach to perform statistical inference for a range of applied problems.
- Apply decision theory to a range of problems.

Students will develop skills across the cognitive domain (Bloom's taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate, and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practical classes are used to help develop the students abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module.

The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections. The examination time allows the students to try different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The project allows the students to develop their problem solving techniques, to practice the methods learnt in the module, to assess their progress and to receive feedback; this assessment has a secondary formative purpose as well as its primary summative purpose.

General Notes

N/A