Decision Theory & Bayesian Statistics - MAT00101H
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 |
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A | Semester 1 2025-26 |
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:
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State and explain the basic concepts of Bayesian inference
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Apply the Bayesian paradigm to basic models of statistical inference using appropriate numerical methods.
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Use the basic ideas of credibility theory to estimate risk in insurance contexts.
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Apply Bayesian inference in the context of decision problems using loss functions.
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.
Indicative assessment
Task | % of module mark |
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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.