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The correspondence between credibilities and induced betting rate assignments

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Abstract

Operational statistics is an operational theory of probability and statistics which generalizes classical probability and statistics and provides a formalism particularly suited to the needs of quantum mechanics. Within this formalism, statistical inference can be accomplished using the Bayesian inference strategy. In a hierarchical Bayesian approach, a second-order probability measure, or credibility, represents degrees of belief in statistical hypotheses. A credibility determines an assignment of simple and conditioned betting rates to events in a natural way. In the setting of operational statistics, we show that a credibility is completely determined by the assignment of the betting rates it induces. This result suggests a certain unity between the Bayesian philosophy which deems that betting rates are central and the one which advocates the hierarchical approach.

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Authors and Affiliations

  1. Department of Mathematics, Kingsbury Hall, University of New Hampshire, 03824, Durham, New Hampshire

    Marie Gaudard

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  1. Marie Gaudard
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Gaudard, M. The correspondence between credibilities and induced betting rate assignments. Found Phys 14, 431–441 (1984). https://doi.org/10.1007/BF00738810

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  • DOI: https://doi.org/10.1007/BF00738810

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