Characterizing the set of coherent lower previsions with a finite number of constraints or vertices

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Abstract

The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation of this criterion that only uses a finite number of constraints. Any such lower prevision is coherent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.

Original languageEnglish
Title of host publicationProceedings of the 26th Conference on Uncertainty in Artificial Intelligence, UAI 2010
EditorsPeter Grünwald, Peter Spirtes
PublisherAUAI Press
Pages466-473
Number of pages8
ISBN (Print)9780974903965
Publication statusPublished - 2010
Externally publishedYes
Event26th Conference on Uncertainty in Artificial Intelligence, UAI 2010 - Catalina Island, CA, United States
Duration: 8 Jul 201011 Jul 2010

Conference

Conference26th Conference on Uncertainty in Artificial Intelligence, UAI 2010
CountryUnited States
CityCatalina Island, CA
Period8/07/1011/07/10

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