BAYESIAN STATISTICS - 2022/3

Module code: MAT3003

Module Overview

The module looks at the branch of statistics called Bayesian Statistics. It relies on subjective probability and looks at why this is extremely useful for modelling realistic problems. The module covers an introduction to Bayesian statistics, incorporating prior to posterior analysis for a wide range of statistical models. This shows the students an alternative approach to the Classical statistics that they have studied so far and looks at various statistical techniques that they have studied before and gives them a Bayesian approach.

Module provider

Mathematics & Physics

Module cap (Maximum number of students): N/A

Independent Learning Hours: 90

Lecture Hours: 27

Laboratory Hours: 6

Captured Content: 27

Semester 1

Prerequisites / Co-requisites

MAT2013 Mathematical Statistics

Module content

Indicative content includes:

• review of distribution theory

• subjective probability and prior distributions – noninformative and conjugate

• prior to posterior analysis

• exponential families, sufficiency and conjugate priors

• predictive inference

• Bayesian estimation and hypothesis testing

• application to linear models

• approximate methods to estimation

• elements of decision theory and comparative inference

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 min) 20
Examination Exam (2 hrs) 80

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·        Understanding of and ability to interpret and manipulate mathematical statements.

·        Subject knowledge through the recall of key definitions, theorems and their proofs.

·        Analytical ability through the solution of unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

·    One examination at the end of the semester; worth 80% of the module mark.

·    One in-semester test; worth 20% of the module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments over an 11 week period. In addition, verbal feedback is provided in tutorial lectures.

Module aims

• introduce the rationale for, the main techniques of, and general issues in Bayesian statistics
• apply techniques to standard statistical models, including exponential families and linear models
• apply Bayesian approaches to estimation and testing
• introduce Bayesian prediction
• consider the role of decision theory

Learning outcomes

 Attributes Developed 001 Analyse the differences between the Bayesian paradigm and frequentist statistical methods KC 002 Calculate the posterior and predictive distribution and related quantities KC 003 Define hierarchical models and state and prove related theorems KC 004 Demonstrate how models can be written in hierarchical form and calculate posterior quantities KCPT 005 Explain the arguments for and against the Bayesian paradigm. KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A detailed introduction to the theory behind, methodology and approaches used in Bayesian statistics

• Experience (through demonstration) of the methods used to interpret, understand and solve problems in analysis

The learning and teaching methods include:

• 3 x 1 hour lectures per week x 6 weeks and 2 x 1 hour lectures per week for 5 hours, with additional notes on white board to supplement the module handbook and Q + A opportunities for students.

• 5 x 1 hour tutorial replaces one of the lectures for guided discussion of solutions to problem sheets provided to and worked on by students during the tutorial.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.