# BAYESIAN INFERENCE FOR DATA SCIENCES - 2023/4

Module code: MAT3052

## 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.

Mathematics

### Module cap (Maximum number of students): 150

Independent Learning Hours: 106

Lecture Hours: 5

Seminar Hours: 11

Laboratory Hours: 6

Guided Learning: 11

Captured Content: 11

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

• predictive inference

• Bayesian estimation and hypothesis testing

• application to linear models

• approximate methods to estimation

• elements of decision theory and comparative inference

• Gibbs sampling

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 25
Examination Final examination 75

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## 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.

• Ability to implement computational Bayesian method and use visualisation tools to present the result via statistical software such as Python

Thus, the summative assessment for this module consists of:

• One two-hour examination; worth 75% module mark.

• One assessed coursework; worth 25% module mark.

Formative assessment and feedback: Students receive written feedback via marked coursework assignment

## Module aims

• Introduce the rationale for, the main techniques of, and general issues in Bayesian statistics
• Apply techniques to standard statistical models such as normal linear models
• Apply Bayesian approaches to estimation and testing
• Introduce Bayesian prediction
• Consider the role of decision theory
• Computational Bayesian technique using Gibbs sampling

## Learning outcomes

 Attributes Developed 001 Analyse the differences between the Bayesian paradigm and frequentist statistical methods CK 002 Calculate the posterior and predictive distribution and related quantities CK 003 Define hierarchical models and state and prove related theorems CK 004 Demonstrate how models can be written in hierarchical form and calculate posterior quantities CKPT 005 Explain the arguments for and against the Bayesian paradigm CK 006 Demonstrate coding skills to apply Bayesian inference to analyse real-world data and predictive analysis PT

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:

• face-to-face seminars and lectures, supported by face-to-face computer lab sessions designed to develop programming skills to apply Bayesian inference to analyse real-world data.

• online recorded material designed to complement the face-to-face sessions.

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.

Upon accessing the reading list, please search for the module using the module code: MAT3052

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## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematical Data Science MSc 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.