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Conglomerable Coherent Lower Previsions

  • Enrique Miranda
  • Marco Zaffalon
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 190)

Abstract

Walley’s theory of coherent lower previsions builds upon the former theory by Williams with the explicit aim to make it deal with conglomerability. We show that such a construction has been only partly successful because Walley’s founding axiom of joint coherence does not entirely capture the implications of conglomerability. As a way to fully achieve Walley’s original aim, we propose then the new theory of conglomerable coherent lower previsions. We show that Walley’s theory coincides with ours when all conditioning events have positive lower probability, or when conditioning partitions are nested.

Keywords

Coherent lower previsions conglomerability sets of desirable gambles Williams’ coherence 

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References

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    de Finetti, B.: Sulla proprietà conglomerativa della probabilità subordinate. Rendiconti del Reale Instituto Lombardo 63, 414–418 (1930)zbMATHGoogle Scholar
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    Miranda, E., Zaffalon, M., de Cooman, G.: Conglomerable natural extension. Int. J. Approx. Reason. (accepted)Google Scholar
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    Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London (1991)zbMATHGoogle Scholar
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    Williams, P.M.: Notes on conditional previsions. Tech. rep., School of Mathematical and Physical Science, University of Sussex, UK (1975); Reprinted in Int. J. Approx. Reason. 44, 366–383 (2007)Google Scholar
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    Zaffalon, M., Miranda, E.: Probability and time (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of OviedoOviedoSpain
  2. 2.IDSIAMannoSwitzerland

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