Search results for "total coherence"

showing 2 items of 2 documents

On general conditional prevision assessments

2009

In this paper we consider general conditional random quantities of the kind $X|Y$, where $X$ and $Y$ are finite discrete random quantities. Then, we introduce the notion of coherence for conditional prevision assessments on finite families of general conditional random quantities. Moreover, we give a compound prevision theorem and we examine the relation between the previsions of $X|Y$ and $Y|X$. Then, we give some results on random gains and, by a suitable alternative theorem, we obtain a characterization of coherence. We also propose an algorithm for the checking of coherence. Finally, we briefly examine the case of imprecise conditional prevision assessments by introducing the notions of…

Conditional random quantities; coherence; conditional prevision assessments; random gain; alternative theorems; algorithms; imprecise assessments; generalized and total coherence.Settore MAT/06 - Probabilita' E Statistica Matematicarandom gainConditional events general conditional random quantitiesgeneral conditional prevision assessments generalized compound prevision theorem generalized Bayes TheoremConditional random quantitiesalgorithmsimprecise assessmentsalternative theoremsgeneralized and total coherencecoherenceconditional prevision assessments
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Coherent conditional probabilities and proper scoring rules

2011

In this paper we study the relationship between the notion of coherence for conditional probability assessments on a family of conditional events and the notion of admissibility with respect to scoring rules. By extending a recent result given in literature for unconditional events, we prove, for any given strictly proper scoring rule s, the equivalence between the coherence of a conditional probability assessment and its admissibility with respect to s. In this paper we focus our analysis on the case of continuous bounded scoring rules. In this context a key role is also played by Bregman divergence and by a related theoretical aspect. Finally, we briefly illustrate a possible way of defin…

total coherenceSettore MAT/06 - Probabilita' E Statistica Matematicabregman divergencestrong dominanceconditional scoring rulesConditional probability assessments coherence penalty criterion proper scoring rules conditional scoring rules weak dominance strong dominance admissibility Bregman divergence g-coherence total coherence imprecise probability assessments.weak dominancestrong dominance; conditional probability assessments; imprecise probability assessments; gcoherence; proper scoring rules; bregman divergence; weak dominance; coherence; imprecise probability assessments.; admissibility; g-coherence; penalty criterion; conditional scoring rules; total coherencepenalty criteriongcoherenceproper scoring rulescoherenceconditional probability assessmentsg-coherenceimprecise probability assessmentsadmissibility
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