Probabilistic coherence and proper scoring rules

Probabilistic coherence and proper scoring rules,10.1109/TIT.2009.2027573,IEEE Transactions on Information Theory,Joel B. Predd,Robert Seiringer,Ellio

Probabilistic coherence and proper scoring rules   (Citations: 7)
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We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and claries the connection of coherence and proper scoring rules to Bregman di- vergence.
Journal: IEEE Transactions on Information Theory - TIT , vol. 55, no. 10, pp. 4786-4792, 2009
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    • ...In [5], a more general formulation of the CAP problem is considered and it is demonstrated that the Euclidean objective function in (1) is not inherent...

    Peter Joneset al. Revision of marginal probability assessments

    • ...[7] established that, for the case of nitely many marginal previsions, de Finetti’s geometric argument extends to all continuous strictly proper scoring rules by generalizing the role played by the Euclidean metric with Brier score to Bregman divergence for continuous scoring rules...
    • ...That is, even if we were to restrict attention solely to marginal previsions, as [7] do, our proofs would still use all of the assumptions in order to deal with the examples in this section...
    • ...Whether or not we can guarantee weak dominance does not depend on whether or not we are using merely proper scoring rules, but rather on a continuity property of the strictly proper scoring rules (Assumption 2). [7] claim that, if one uses continuous merely proper scoring rules, one can guarantee a weakly dominating coherent1 set of forecasts...

    Mark J. Schervishet al. Proper Scoring Rules, Dominated Forecasts, and Coherence

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