MAS2903 : Introduction to Bayesian methods
- Offered for Year: 2022/23
- Module Leader(s): Dr Lee Fawcett
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
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 Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures – Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures – Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes – Synchronous On-Line |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Guided Independent Study | Assessment preparation and completion | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 5 | 1:00 | 5:00 | Synchronous On-Line |
| Total | 100:00 |
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 Examination | 120 | 2 | A | 80 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 10 | Problem-solving exercises |
| Prob solv exercises | 2 | M | 10 | Problem-solving exercises |
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
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS2903's Timetable