Undergraduate

modules

Modules

MAS2903 : An Introduction to Bayesian methods

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

Students will learn about the Bayesian approach to statistical analysis. Students will be able to explain the distinctive features of Bayesian methodology, understand the role of prior distributions and compute posterior distributions in simple cases.

Module summary

The module will be devoted to an introduction to Bayesian methods, in which the prior and posterior distributions of a scalar parameter will be defined. The use of the likelihood to allow the prior distribution to be updated to the posterior distribution will be discussed. The use of Bayes theorem to compute posterior distributions from given priors and likelihoods will be described, with particular emphasis given to the case of conjugate distributions.

Outline Of Syllabus

Introduction to the Bayesian approach: subjective probability; likelihood; sufficiency. Inference for populations using random samples and conjugate priors, including posterior estimates and highest density intervals: inference for the mean of a normal distribution with known variance; inference for parameters in other commonly used distributions. Sequential use of Bayes' Theorem. Parameter constraints. Mixture prior distributions. Asymptotic posterior distribution.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study123:0023:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework assignments
Prob solv exercises2M10Course test
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of two written assignment of approximately equal weight. The coursework assignments and the (in class) coursework test 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 are thus formative as well as summative assessments.

Reading Lists

Timetable