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Decision Theory & Bayesian Statistics - MAT00114M

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: M
• Academic year of delivery: 2024-25
  • See module specification for other years: 2023-24

Module summary

This module develops the basics of the Bayesian approach to statistics and studies its applicability to statistical inference. In addition, the Bayesian approach will be applied to model decisions under uncertainty through its integration with the theory of expected utility.

Professional requirements

Counts towards IFoA exemption.

Related modules

Module will run

Occurrence	Teaching period
A	Semester 1 2024-25

Module aims

This module develops the basics of the Bayesian approach to statistics and studies its applicability to statistical inference. In addition, the Bayesian approach will be applied to model decisions under uncertainty through its integration with the theory of expected utility.

Module learning outcomes

By the end of the module students will be able to:

1. State and explain the basic concepts of Bayesian inference

2. Apply the Bayesian paradigm to basic models of statistical inference using appropriate numerical methods.

3. Use the basic ideas of credibility theory to estimate risk in insurance contexts.

4. Apply Bayesian inference in the context of decision problems using loss functions.

5. (M-level) Carry out self-directed learning.

Module content

We discuss the basic idea of Baysian inference, i.e., the combination of prior information and data to draw inferences. This will be applied to some commonly-used inferential models, in the context of which some numerical, simulation-based, methods are developed. As a particular area of application we study credibility theory, which is important for actuaries in estimating risk. In the second part of the module, we develop the theory of expected utility and apply it to decision problems under uncertainty. Finally, decision theory and Bayesian inference are combined in the study of decision problems under uncertainty with data availability.

The M-level students will be provided with some self-directed learning material on an advanced topic (e.g. hierarchical models, maximin decision theory), which will be assessed in the exam.

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

Berger (1985), “Statistical Decision Theory and Bayesian Analysis”, Springer Verlag.

Gilboa (2009), “Theory of Decision under Uncertainty”, Cambridge University Press.

Hoff (2009), “A First Course in Bayesian Statistical Methods”, Springer Verlag.

Lee (2012), “Bayesian Statistics”, Wiley & Sons.