Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

To develop further an understanding of Bayesian inference, to gain knowledge of modern applications of Bayesian inference and modern Bayesian computational methods and to acquire skill in Bayesian modelling, data analysis and computation.

Module summary

In recent years great advances have been made in the application of Bayesian statistical inference to problems in a wide variety of areas. This has been made possible by the development of computational algorithms which allow posterior distributions to be found in complicated models. This module extends the introductory material on Bayesian inference given in MAS3902 and, in particular, look at more complex models.

Outline Of Syllabus

Review of Bayesian inference, particularly non-conjugate scenarios. Introduction to Monte Carlo methods. Review of Markov chain Monte Carlo (MCMC), including Gibbs sampling and Metropolis-Hastings; assessment of mixing and convergence. Theoretical foundations of MCMC. Some advanced topics in computational statistics covered may include Approximate Bayesian computation and Sequential Monte Carlo methods.

Applications considered may include: linear models, generalized linear models, missing data problems, data augmentation, mixture models and hierarchical models.

Intended Knowledge Outcomes

On completion of the course, students will be familiar with the theory and practicalities of computational methods and will have a knowledge of the application of these ideas in a range of problem types.

Intended Skill Outcomes

Students will have increased statistical computing skills and enhanced report writing skills. They will be able to construct a range of computational algorithms suitable for a variety of models and implement these using appropriate software. They will be able to use this knowledge to make inferences from data in such cases.

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. Problem Classes and computer practicals 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, while they may have more than one ways for solution. The examination time allows the students to test 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 coursework assignments and in-class tests allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

N/A