Aims

To gain an understanding of the principles and the practical applications of Bayesian Statistics to more complex models relevant to practical data analysis. To improve data-analytic and report-writing skills through group project work.

Module summary

The course builds on the foundations of Bayesian inference laid in MAS2903. We consider extensions to models with more than a single parameter and how these can be used to analyse data. We also provide an introduction to modern computational tools for the analysis of more complex models for real data.

Outline Of Syllabus

Review of Bayesian inference for single parameter models. Inference for multi-parameter models using conjugate prior distributions: mean and variance of a normal random sample. Asymptotic posterior distribution for multi-parameter models. Introduction to Markov chain Monte Carlo methods: Gibbs sampling, Metropolis-Hastings sampling, mixing and convergence. Application to random sample models using conjugate and non-conjugate prior distributions. Computation using R.

Teaching Rationale And Relationship

The teaching method 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 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 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.