Search results for " reduced sets of variables"

showing 3 items of 3 documents

On the checking of g-coherence of conditional probability bounds

2003

We illustrate an approach to uncertain knowledge based on lower conditional probability bounds. We exploit the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), which is equivalent to the "avoiding uniform loss" property introduced by Walley for lower and upper probabilities. Based on the additive structure of random gains, we define suitable notions of non relevant gains and of basic sets of variables. Exploiting them, the linear systems in our algorithms can work with reduced sets of variables and/or constraints. In this paper, we illustrate the notions of non relevant gain and of basic set by examining several cases of imprecise assessments d…

Mathematical optimizationSettore MAT/06 - Probabilita' E Statistica MatematicaPosterior probabilityConditional probability tablealgorithmslower conditional probability boundRegular conditional probabilityalgorithms; generalized coherence; linear systems; lower conditional probability bounds; probabilistic reasoning; reduced sets of variables and constraints.Artificial Intelligencelinear systemprobabilistic reasoninggeneralized coherenceMathematicsDiscrete mathematicsreduced sets of variables and constraintsalgorithmlinear systemsProbabilistic logicLaw of total probabilityConditional probabilityCoherence (philosophical gambling strategy)Conditional probability distributionControl and Systems Engineeringlower conditional probability boundsSoftwareInformation Systems
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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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Algorithms for coherence checking and propagation of conditional probability bounds

2001

In this paper, we propose some algorithms for the checking of generalized coherence (g-coherence) and for the extension of imprecise conditional probability assessments. Our concept of g-coherence is a generalization of de Finetti’s coherence principle and is equivalent to the ”avoiding uniform loss” property for lower and upper probabilities (a la Walley). By our algorithms we can check the g-coherence of a given imprecise assessment and we can correct it in order to obtain the associated coherent assessment (in the sense of Walley and Williams). Exploiting some properties of the random gain we show how, in the linear systems involved in our algorithms, we can work with a reduced set of va…

reduced sets of variables and constraintsSettore MAT/06 - Probabilita' E Statistica MatematicaUncertain knowledgeUncertain knowledge probabilistic reasoning under coherence imprecise conditional probability assessments g-coherence checking g-coherent extension algorithms computational aspects reduced sets of variables reduced sets of linear constraints.g-coherent extensionimprecise conditional probability assessmentsg-coherence checkingUncertain knowledge; probabilistic reasoning under coherence; imprecise conditional probability assessments; g-coherence checking; g-coherent extension; algorithms.; computational aspects; reduced sets of variables and constraints.algorithmsprobabilistic reasoning under coherencecomputational aspects
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