0000000000421692

AUTHOR

V. Biazzo

showing 3 related works from this author

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.
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Computational aspects in checking of coherence and propagation of conditional probability bounds

2000

In this paper we consider the problem of reducing the computational difficulties in g-coherence checking and propagation of imprecise conditional probability assessments. We review some theoretical results related with the linear structure of the random gain in the betting criterion. Then, we propose a modi ed version of two existing algorithms, used for g-coherence checking and propagation, which are based on linear systems with a reduced number of unknowns. The reduction in the number of unknowns is obtained by an iterative algorithm. Finally, to illustrate our procedure we give some applications.

reduced sets of variables and constrainsCoherent probability assessments propagation random gain computation algorithmsSettore MAT/06 - Probabilita' E Statistica MatematicaChecking of coherencerandom gainpropagationChecking of coherence; computational aspects; propagation; linear systems; random gain; reduced sets of variables and constrainslinear systemscomputational aspects
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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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