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Axiomatising the Bayesian paradigm in parallel small worlds
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French, Simon (2020) Axiomatising the Bayesian paradigm in parallel small worlds. Operations Research, 70 (3). pp. 1342-1358. doi:10.1287/opre.2019.1896 ISSN 0030-364X.
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Official URL: https://doi.org/10.1287/opre.2019.1896
Abstract
There is currently much interest in scenario-focused decision analysis (SFDA), a methodology which provides, among other things, supporting analyses in circumstances in which there are deep uncertainties about the future, i.e. when experts and decision makers (DMS) cannot come to any agreement on some of the probabilities to use in a Bayesian model. This lack of agreement can mean that sensitivity and robustness analyses show that virtually any strategy may be optimal under the beliefs of one or more participants. Scenario-focused analyses fix the deep uncertainties at interesting values in different scenarios and conduct a (Bayesian) decision analysis within each. The results can be informative to the DMS, helping them understand different possible futures and their reactions to them. However, theoretical axiomatisations of subjective expected utility (SEU), the core of decision analysis, do not immediately extend to the context of SFDA. The purpose of this paper is to provide an axiomatisation of SEU that supports SFDA. Scenarios have much in common with Savage’s concept of a small worlds. We discuss the parallels and then explore two difficulties in extending his and other writers’ axiomatisations. The development of SEU offered here overcomes these difficulties. Throughout attention is given to the implications of the theoretical development for the practice of decision analysis.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Uncertainty -- Mathematical models | ||||||||||||
Journal or Publication Title: | Operations Research | ||||||||||||
Publisher: | Institute for Operations Research and the Management Sciences (I N F O R M S) | ||||||||||||
ISSN: | 0030-364X | ||||||||||||
Official Date: | 2020 | ||||||||||||
Dates: |
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Volume: | 70 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 1342-1358 | ||||||||||||
DOI: | 10.1287/opre.2019.1896 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | Copyright © 2020, INFORMS | ||||||||||||
Date of first compliant deposit: | 11 June 2019 | ||||||||||||
Date of first compliant Open Access: | 12 June 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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