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We study, from the standpoint of coherence, comparative probabilities on an arbitrary familyE of conditional events. Given a binary relation ·, coherence conditions on · are related to de Finetti's coherent betting system: we consider their connections to the usual properties of comparative probability and to the possibility of numerical representations of ·. In this context, the numerical reference frame is that of de Finetti's coherent subjective conditional probability, which is not introduced (as in Kolmogoroff's approach) through a ratio between probability measures.Another relevant feature of our approach is that the family & need not have any particular algebraic structure, so that the ordering can be initially given for a few conditional events of interest and then possibly extended by a step-by-step procedure, preserving coherence. 相似文献
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Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion
that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference.
Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and
Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy. 相似文献
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We propose two different characterizations for preference relations representable by lower (upper) expectations with the aim
of removing either fair price or completeness requirements. Moreover, we give an explicit characterization for comparative
degrees of belief on a finite algebra of events representable by lower probabilities. 相似文献
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Statistical Methods & Applications - Starting from a likelihood function and a prior information represented by a belief function, a closed form expression is provided for the lower envelope of... 相似文献
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Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing
only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional
events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the
case of binary relations representable by a coherent conditional probability. 相似文献
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We introduce a rationality principle for a preference relation on an arbitrary set of lotteries. Such a principle is a necessary and sufficient condition for the existence of an expected utility agreeing with . The same principle also guarantees a rational extension of the preference relation to any larger set of lotteries. When the extended relation is unique with respect to the alternatives under consideration, the decision maker does not need a numerical evaluation in order to make a choice. Such a rationality condition needs little information in order to be applied, and its verification amounts to solving a linear system.The present research is supported by the Research Contract of CNR (Research National Council) 1989 and 1990 Decision Models under uncertainty and risk, for expert systems with incomplete and revisable information. 相似文献
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