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Module

MAS2903 : Introduction to Bayesian methods

  • Offered for Year: 2023/24
  • Module Leader(s): Mr Matthew Fisher
  • 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.

Semester 2 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

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 ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion531:0053:00Preparation time for lectures, background reading, coursework review
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00n/a
Total100:00
Teaching Rationale And Relationship

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. 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 Examination1202A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
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.

Reading Lists

Timetable