1,721,017 research outputs found
Review of MR2731982: Fedel, Martina(I-SIN-MI) - Uncertainty, indeterminacy and fuzziness: a probabilistic approach. Probability, uncertainty and rationality, 219–242, CRM Series, 10, Ed. Norm., Pisa, 2010.
No full textThe paper presents an interesting generalisation of some results about de Finetti coherent probabilities to an assignment of indeterminate probabilities on many-valued events in an MV-algebra. After recalling the Dutch Book interpretation of probability by de Finetti and his well-known related theorem, which states that an agent's degrees of belief are coherent (i.e. they do not permit a Dutch Book) if and only if they conform to probability axioms, the author proves an analogous result for upper (and lower) probabilities defined on divisible MV-algebras. Specifically, she proves that in a divisible MV-algebra of events a book does not allow any bad bet if and only if it can be extended to an upper probability over the whole MV-algebra. The proof of this result relies on Hahn-Banach and separation theorems as well as on other tools from functional analysis
Review of MR2545545 - Halpern, Joseph Y.; Pucella, Riccardo - Evidence with uncertain likelihoods. Synthese 171 (2009), no. 1, 111–133.
No full textIn the standard literature on evidence, a customary assumption provides for the existence of a single likelihood function associated to each agent's hypothesis. In this paper the authors start from the consideration that in many practical situations this assumption raises some issues when using evidence for making decisions. Therefore, they supply a new general framework which allows the reader to deal with the case of uncertain likelihood functions. The authors' approach is consistent with Shafer's approach to handling evidence. Many examples and the deferring of technical proofs to an appendix make the reading easier
Some remarks on the use of strict complementarity in checking coherence and extending coherent probabilities
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An Applications of Unsupervised Neural Networks in General Insurance: the Determination of Tariff Classes
No full textBayes Theorem Bounds for Convex Lower Previsions
No full textIn this paper we consider some bounds for lower previsions that are either coherent or, more generally, centered convex. We focus on bounds concerning the classical product and Bayes’ rules, discussing first weak product rules and some of their implications for coherent lower previsions. We then generalise a well-known lower bound, which is a (weak) version for events and coherent lower probabilities of Bayes’ theorem, to the case of random variables and (centered) convex previsions. We
obtain a family of bounds and show that one of them is undominated in all cases. Some applications are outlined, and it is shown that 2-monotonicity, which ensures that the bound is sharp in the case of events, plays a much more limited role in this general framework
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