Search results for "conditional prevision assessments"

showing 3 items of 3 documents

Coherent Conditional Previsions and Proper Scoring Rules

2012

In this paper we study the relationship between the notion of coherence for conditional prevision assessments on a family of finite conditional random quantities and the notion of admissibility with respect to bounded strictly proper scoring rules. Our work extends recent results given by the last two authors of this paper on the equivalence between coherence and admissibility for conditional probability assessments. In order to prove that admissibility implies coherence a key role is played by the notion of Bregman divergence.

Settore MAT/06 - Probabilita' E Statistica Matematicabregman divergenceproper scor- ing rulesConditional prevision assessmentsconditional scoring rulesstrong dominanceConditional probabilityweak dominanceCoherence (statistics)Bregman divergenceConditional prevision assessments coherence proper scoring rules conditional scoring rules weak dominance strong dominance admissibility Bregman divergence.proper scoring rulescoherenceBounded functionKey (cryptography)admissibilityConditional prevision assessments; conditional scoring rules; admissibility; proper scor- ing rules; weak dominance; strong dominanceEquivalence (measure theory)Mathematical economicsconditional prevision assessments; strong dominance; admissibility; proper scoring rules; bregman divergence; weak dominance; conditional scoring rules; coherenceMathematics
researchProduct

On general conditional random quantities

2009

In the first part of this paper, recalling a general discussion on iterated conditioning given by de Finetti in the appendix of his book, vol. 2, we give a representation of a conditional random quantity $X|HK$ as $(X|H)|K$. In this way, we obtain the classical formula $\pr{(XH|K)} =\pr{(X|HK)P(H|K)}$, by simply using linearity of prevision. Then, we consider the notion of general conditional prevision $\pr(X|Y)$, where $X$ and $Y$ are two random quantities, introduced in 1990 in a paper by Lad and Dickey. After recalling the case where $Y$ is an event, we consider the case of discrete finite random quantities and we make some critical comments and examples. We give a notion of coherence fo…

Settore MAT/06 - Probabilita' E Statistica Matematicageneral conditional random quantities; general conditional prevision assessments; generalized compound prevision theoremgeneral conditional prevision assessmentsiterated conditioninggeneralized compound prevision theoremgeneral conditional random quantitiesconditional eventsstrong generalized compound prevision theoremConditional events general conditional random quantities general conditional prevision assessments generalized compound prevision theorem iterated conditioning strong generalized compound prevision theoremconditional events; general conditional random quantities; general conditional prevision assessments; generalized compound prevision theorem; iterated conditioning; strong generalized compound prevision theorem.
researchProduct

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
researchProduct