Global Opportunities

### MAS2903 : Introduction to Bayesian methods

• Offered for Year: 2021/22
• Incoming Study Abroad and Exchange students must contact and seek approval from school prior to enrolling
• 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 ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Guided Independent StudyAssessment preparation and completion531:0053:00Preparation time for lectures, background reading, coursework review
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Synchronous On-Line
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.

#### 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 exercises2M10Problem-solving exercises
Prob solv exercises2M10Problem-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.