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Module

MAS8384 : Bayesian Methodology

  • Offered for Year: 2021/22
  • Module Leader(s): Dr Murray Pollock
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

Bayesian inference provides an ideal approach for synthesizing information from different sources in a coherent way. In recent years great advances have been made in the application of Bayesian statistical inference to problems across a wide variety of areas within industry, such as drug development, voice recognition and credit card fraud detection. This has been made possible by the development of computational algorithms which allow posterior distributions to be found in complicated models. This module starts with an introduction to the principles of Bayesian inference before moving on to address the fundamental practical problem of calculating the posterior distribution for complex models. The theory behind some modern Bayesian computational methods, which provide a simulation-based solution, is developed and put into practice using R.

Specifically, the module aims to equip students with the following knowledge and skills:
- To gain an understanding of the principles of the Bayesian approach to inference and experience in the application of Bayes rule to update a prior distribution to a posterior distribution using a likelihood function.
- To gain an understanding of the theory behind some modern Bayesian computational methods for approximating a posterior distribution and practical experience of their application in R to solve a variety of applied problems.

Outline Of Syllabus

- Conjugate Bayesian inference
- Non-conjugate models
- Markov chain Monte Carlo (MCMC): methods such as Gibbs sampling, Metropolis-Hastings sampling, slice sampling; assessment of mixing and convergence
- Posterior summaries
- Applications, such as linear models, generalized linear models, mixture models, hidden Markov models, dynamic linear models, Gaussian process regression
- Computation using R and R packages such as rjags

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Structured Guided LearningLecture materials91:3013:30Non-synchronous online pre-recorded lectures and set reading
Guided Independent StudyAssessment preparation and completion214:0028:00Formative and summative reports
Scheduled Learning And Teaching ActivitiesPractical62:0012:00Present in person structured synchronous practical
Guided Independent StudyProject work129:0029:00Main project
Scheduled Learning And Teaching ActivitiesDrop-in/surgery22:004:00Present in person drop-in
Guided Independent StudyIndependent study91:3013:30Lecture follow up/background reading
Total100:00
Teaching Rationale And Relationship

Pre-recorded lectures and set reading are used for the delivery of theory and explanation of methods, illustrated with examples. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied. There are two present-in-person practical sessions per week to ensure rapid feedback on understanding. Scheduled present-in-person drop-ins provides opportunity to ask questions and receive immediate feedback. Students unable to attend PiP will be able to complete the practical work at home and will be able to receive immediate feedback through joining the drop-ins virtually.

Alternatives as described will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.

Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

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

Other Assessment
Description Semester When Set Percentage Comment
Practical/lab report2M40Individual report
Report2M60Main module project
Zero Weighted Pass/Fail Assessments
Description When Set Comment
Oral PresentationMA 3 min video articulating the main findings of one aspect of the coursework report
Formative Assessments
Description Semester When Set Comment
Practical/lab report2MA compulsory report allowing students to develop problem solving techniques, to practise the methods learnt and to assess progress
Assessment Rationale And Relationship

A compulsory formative practical report allows the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback, before the summative assessments.

The oral presentation encourages students to focus on interpretation of statistical results, builds their skills in the presentation of statistical concepts, and provides opportunity for feedback.

In a foundational subject like the Mathematical Sciences, there is research evidence to suggest that continual consolidation of learning is essential and the fewer pieces of assessment there are, the more difficult it is to facilitate this. On this module, it is particularly important that the material on the earlier summative assessment is fully consolidated, before the later assessment is attempted.

Reading Lists

Timetable