ST301 Bayesian Statistics and Decision Theory
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ST30115 Bayesian Statistics and Decision Theory
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. It 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.
Prerequisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
NonStatistics 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/payoff 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.
Learning outcomes
By the end of the module, students should be able to:
 To understand how Bayesian models are built and evaluated. Appreciate idiot Bayes models and issues such as calibration.
 To perform basic prior to posterior analysis. To perform discrete prior to posterior inference and beta and Dirichlet conjugate analysis.
 To understand the foundation of utility theory and apply it in a multiattribute context. To be able to elicit a utility function.
 To understand how to model complicated systems in terms of conditional independences. To appreciate the structuring of models through DAGs. To be able to estimate probabilities in DAGs using conjugate product Dirichlet distributions.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  30 sessions of 1 hour (20%)  2 sessions of 1 hour 
Tutorials  3 sessions of 1 hour (2%)  
Private study  117 hours (78%)  
Total  150 hours 
Private study description
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 B2
Weighting  Study time  

Oncampus Examination  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Assessment group R1
Weighting  Study time  

Online Examination  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Feedback on assessment
Solutions and cohort level feedback will be provided for the examination.
Antirequisite modules
If you take this module, you cannot also take:
 ST41315 Bayesian Statistics and Decision Theory with Advanced Topics
Courses
This module is Optional for:
 Year 3 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 3 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 4 of UCSAG4G2 Undergraduate Discrete Mathematics with Intercalated Year

USTAG300 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
 Year 3 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 4 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
This module is Core option list A for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 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 3 of USTAG302 Undergraduate Data Science
 Year 3 of USTAG304 Undergraduate Data Science (MSci)
 Year 4 of USTAG303 Undergraduate Data Science (with Intercalated Year)

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 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)
 Year 3 of USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 4 of USTAGG17 Undergraduate Mathematics and Statistics (with Intercalated Year)
 Year 3 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 4 of USTAY603 Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year)
This module is Option list B for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 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
 Year 3 of UMAAG100 Undergraduate Mathematics (BSc)

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list E for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
This module is Option list F for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 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)