ST301-15 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.

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 web page

Module aims

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.

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 multi-attribute 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