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Module

MAS8951 : Modern Bayesian Inference

  • Offered for Year: 2021/22
  • Module Leader(s): Dr Daniel Henderson
  • Lecturer: Dr Murray Pollock
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 Credit Value: 15
Semester 2 Credit Value: 15
ECTS Credits: 15.0

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 MAS3914 and, in particular, looks at more complex models.

Outline Of Syllabus

Review of Bayesian inference. Review of Markov chain Monte Carlo (MCMC), including Gibbs sampling and Metropolis-Hastings; assessment of mixing and convergence. Theoretical foundations of MCMC. Approximate Bayesian computation. Sequential Monte Carlo methods, including bootstrap particle filter, issues of degeneracy.

Applications, such as: linear models, generalized linear models, missing data problems, data augmentation, mixture models, dynamic linear models, random effects and hierarchical models.

Computation using rjags package within R.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture601:0060:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture61:006:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture151:0015:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion401:0040:00Completion of in course assessments
Guided Independent StudyIndependent study1791:00179:00Preparation time for lectures, background reading, coursework review
Total300:00
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.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1502A60N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M20Coursework assignment
Prob solv exercises2M20Coursework assignment
Assessment Rationale And Relationship

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

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists

Timetable