# BAYESIAN INFERENCE FOR DATA SCIENCES - 2024/5

Module code: MAT3052

## Module Overview

Bayesian Statistics is the branch of statistics that relies on subjective probability to create a wide range of statistical models. This module introduces Bayesian methodology and guides students to use prior to posterior analysis for modelling realistic problems. This module then tackles more difficult topics such as Bayesian point estimates, model selection and linear regression.

### Module provider

Mathematics & Physics

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

Independent Learning Hours: 75

Lecture Hours: 27

Laboratory Hours: 6

Guided Learning: 15

Captured Content: 27

Semester 1

N/A

## Module content

Indicative content includes:

• Subjective probability and prior distributions, including noninformative and conjugate priors;

• Prior to posterior analysis and predictive inference;

• Standard models: Binomial, Poisson, Normal and Mixtures;

• Asymptotic normal approximation of posteriors;

• Bayesian parameter estimation using loss functions;

• Bayesian model selection using Bayes Factor;

• Bayesian linear regression;

• Introduction to computational techniques using Gibbs sampling.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 25
Examination Final examination (2 hr) 75

N/A

## Assessment Strategy

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

• Understanding, interpretation and manipulation of mathematical statements.

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

• Analytical ability to model unseen problems in the test and exam and calculate probabilities, estimate parameters and choose models.

• Ability to implement computational Bayesian methods and use visualisation tools to present the results using statistical software.

Thus, the summative assessment for this module consists of:

• One coursework involving analysis using statistical software, worth 25% of the module mark, corresponds to Learning Outcomes 1, 2, 5.

• A synoptic examination (2 hours), worth 75% of the module mark, corresponds to Learning Outcomes 1, 2, 3, 4.

Formative assessment

There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback

Individual written feedback is provided to students for formative unassessed courseworks. The feedback is timed such that feedback from the first coursework will assist students with preparation for the assessed coursework. The feedback from both courseworks and the assessed coursework will assist students with preparation for the synoptic examination. Students also receive verbal feedback during lectures and computer lab sessions.

## Module aims

• Introduce students to the main techniques of Bayesian statistics and enable them to model realistic problems.
• Give students a thorough understanding of the rationale and general issues of Bayesian techniques.
• Equip students with the tools to apply Bayesian approaches to estimation, testing and prediction in a wide variety of models.
• Introduce students to decision theory and computational Bayesian techniques.

## Learning outcomes

 Attributes Developed 001 Students will understand the differences between Bayesian and frequentist statistical methods and explain the arguments for and against each method. KC 002 Students will be able to calculate the posterior and predictive distribution using Bayes formula. KCT 003 Students will be able to estimate parameters using loss functions and choose between models using the Bayes factor. KCT 004 Students will understand Bayesian linear regression and quote, prove and apply related theorems. KC 005 Students will be able to demonstrate coding skills to apply Bayesian inference to analyze real-world data and predictive analysis. KCPT

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:

Give a detailed introduction to methodology used in Bayesian statistics and ensure experience in the methods used to interpret, understand and solve problems in statistics.

The learning and teaching methods include:

• Two or three one-hour lectures per week for eleven weeks (27 hours total), with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• Six one-hour computer lab sessions in which students gain practical experience of analysing data sets using R.

• Four exercise sheets to reinforce their understanding and guide their learning. These sheets allow students to tackle questions at their own pace outside of scheduled teaching sessions. Model solutions are provided after students have attempted the questions.

• Two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students the opportunity to review parts of lectures that they may not fully have understood and should not be seen as an alternative to attending lectures.

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

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

• Digital Capabilities: The computer lab sessions and assessed coursework in MAT3052 are specifically designed to help students cultivate basic programming skills using statistical software such as R and Python.

• Employability: The computer lab sessions and assessed coursework in MAT3052 are specifically designed to help students cultivate programming skills, gain experience in modelling real data and creating predictive distributions. The specific experience in Bayesian techniques is vital in many attention-grabbing machine learning models.

• Global and Cultural Capabilities: Students enrolled in MAT3052 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures.

• Resourcefulness and Resilience: MAT3052 teaches students analytical skills to tackle uncertainty. The statistical proficiency gained from taking the module sharpens their problem-solving abilities. This gives students tools to complete challenging assignments and thus builds their resourcefulness and resilience.

• Sustainability: Students enrolled in MAT3052 learn to make data-driven decisions in a vast variety of areas, including management of scarce resources and climate science.

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 2024/5 academic year.