• Offered for Year: 2025/26

• Module Leader(s): Dr Lee Fawcett

• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus

Semesters

Your programme is made up of credits, the total differs on programme to programme.

Aims

This module provides a comprehensive introduction to Bayesian statistical modelling, beginning with fundamental concepts such as prior and posterior distributions, Bayes’ theorem, and conjugate priors in simple models. It then extends to more complex models involving multiple parameters and hierarchical structures, with a focus on practical data analysis. A key component of the module is the introduction of computational methods, particularly Markov chain Monte Carlo (MCMC) techniques such as Gibbs sampling and the Metropolis-Hastings algorithm. Students will gain hands-on experience with modern statistical software, developing their skills in data analysis.

Outline Of Syllabus

Introduction to the Bayesian approach to statistics: subjective probability; likelihood; sufficiency. Inference for populations using random samples and conjugate priors, including posterior estimates and highest density intervals: inference for single parameters in commonly used distributions. Sequential use of Bayes' Theorem. Asymptotic posterior distribution for single parameter models. Inference for multi-parameter models using conjugate prior distributions. Asymptotic posterior distribution for multi-parameter models. Introduction to Markov chain Monte Carlo methods: Gibbs sampling, Metropolis-Hastings sampling, practical aspects of mixing and convergence. Application to random sample models using conjugate and non-conjugate prior distributions. Applications may include: linear models, generalized linear models, missing data problems, data augmentation, mixture models, dynamic linear models, and hierarchical models. Computation using R.

Teaching Methods

Teaching Activities

Teaching Rationale And Relationship

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. Practical classes are used to help the students’ ability to apply the methods in practice.

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.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams

Other Assessment

Formative Assessments

Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.

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.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way 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; the summative assessment has a secondary formative purpose as well as its primary summative purpose.

Reading Lists

• DSC8007's Reading List

Timetable

• Timetable Website: www.ncl.ac.uk/timetable/
• DSC8007's Timetable