# ST413-15 Bayesian Statistics and Decision Theory with Advanced Topics

22/23
Department
Statistics
Level
Yi Yu
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### Introductory description

This module runs in Term 1 and aims to demonstrate how to build Bayesian models and to train students in the rudiments of decision analysis.

Students will be given advanced material on causality for independent study and examination.

This module is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.

Pre-requisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
Non-Statistics Students: ST220 Introduction to Mathematical Statistics

Results from this module can be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries (IFoA) module CS1 Actuarial Statistics.

##### Module aims

Bayesian statistics is one of the fastest growing areas in statistics. With the advance of computer technology it is now a highly practical methodology for addressing many important high dimensional decision problems as well as being underpinned by a sound mathematical foundation. It is especially useful when some of the components of uncertainty have only sparsely collected data associated with them, so that expert judgements need to be incorporated.

##### Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Loss/pay-off functions.
• Posterior updating.
• Idiot Bayes.
• Decision trees and the extensive form solution.
• Utility functions — use and elicitation.
• Multiattribute utility functions.
• Forecast scoring.
• The normal form solution.
• DAGS.
• Conjugate priors.
• Causality.
##### Learning outcomes

By the end of the module, students should be able to:

• Understand how Bayesian models are built and evaluated. Appreciate idiot Bayes models and issues such as calibration.
• Perform basic priors to posterior analyses. To perform discrete priors to posterior inference and Beta and Dirichlet conjungate analyses.
• Understand the foundation of utility theory and apply it in a multi-attribute context. Be able to elicit a utility function.
• Understand qualitative widely in terms of conditional independence. Appreciate the structuring of models through DAGs. Be able to estimate probabilities in DAGs using conjugate product Dirichlet distributions.
• Understand by independent study selected advanced research material.

TBC

TBC

## Study time

Type Required Optional
Lectures 30 sessions of 1 hour (20%) 2 sessions of 1 hour
Tutorials 4 sessions of 1 hour (3%)
Private study 116 hours (77%)
Total 150 hours
##### Private study description

Study of advanced topic, weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.

## Costs

No further costs have been identified for this module.

You must pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

##### Assessment group B3
Weighting Study time
In-person Examination 100%

The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade.

• Answerbook Pink (12 page)
• Students may use a calculator
##### Assessment group R2
Weighting Study time
In-person Examination - Resit 100%

The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade.

• Answerbook Pink (12 page)
• Students may use a calculator
##### Feedback on assessment

Solutions and cohort level feedback will be provided for the examination.

##### Anti-requisite modules

If you take this module, you cannot also take:

• ST301-15 Bayesian Statistics and Decision Theory

## Courses

This module is Optional for:

• TMAA-G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
• Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
• Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
• Year 1 of TMAA-G1PF Postgraduate Taught Mathematics of Systems
• Year 1 of TSTA-G4P1 Postgraduate Taught Statistics
• USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
• Year 4 of G300 Mathematics, Operational Research, Statistics and Economics

This module is Core option list A for:

• USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
• Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
• USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
• Year 3 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
• Year 4 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int

This module is Option list A for:

• Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
• USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
• Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
• Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)
• USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
• Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
• Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

This module is Option list B for:

• Year 4 of USTA-G304 Undergraduate Data Science (MSci)
• Year 4 of UCSA-G4G3 Undergraduate Discrete Mathematics
• Year 3 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
• Year 3 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
• Year 4 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int

This module is Option list E for:

• Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

This module is Option list F for:

• Year 3 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
• Year 3 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
• Year 4 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)

Assessments dates for Statistics modules, including coursework and examinations, can be found in the Statistics Assessment Handbook.