Search results for "conditional probability bounds"

showing 4 items of 4 documents

Some results on generalized coherence of conditional probability bounds

2003

Based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of g-coherence is equivalent to the 'avoiding uniform loss' property for lower and upper probabilities (a la Walley). Moreover, given a g-coherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking g-coherence and propagating tight g-coherent intervals are NP and FP^NP complete, respectively, and thus NP-hard. Two notions which may be helpful to reduce co…

g-coherenceUncertain knowledge; coherence; g-coherence; imprecise probabilities; conditional probability bounds; lower and upper probabilities; non relevant gains; basic sets.Settore MAT/06 - Probabilita' E Statistica Matematicanon relevant gainsUncertain knowledgeconditional probability boundslower and upper probabilitiesbasic setsimprecise probabilitiesUncertain knowledge coherence g-coherence imprecise probabilities conditional probability bounds lower and upper probabilities non relevant gains basic setscoherence
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Logical Conditions for Coherent Qualitative and Numerical Probability Assessments

2003

Settore MAT/06 - Probabilita' E Statistica Matematicalower and upper probability boundsUncertain knowledge coherence g-coherence imprecise probabilities conditional probability bounds lower and upper probabilities coherent qualitative probability assessmentsqualitative probabilitieslogical conditionsGeneralized coherenceGeneralized coherence; lower and upper probability bounds; logical conditions; qualitative probabilities.
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Coherence Checking and Propagation of Lower Probability Bounds

2003

In this paper we use imprecise probabilities, based on a concept of generalized coherence (g-coherence), for the management of uncertain knowledge and vague information. We face the problem of reducing the computational difficulties in g-coherence checking and propagation of lower conditional probability bounds. We examine a procedure, based on linear systems with a reduced number of unknowns, for the checking of g-coherence. We propose an iterative algorithm to determine the reduced linear systems. Based on the same ideas, we give an algorithm for the propagation of lower probability bounds. We also give some theoretical results that allow, by suitably modifying our algorithms, the g-coher…

Probability boxMathematical optimizationSettore MAT/06 - Probabilita' E Statistica MatematicaPosterior probabilitynon relevant gainLaw of total probabilityConditional probabilitybasic setsbasic sets; basic sets.; g-coherence checking; lower conditional probability bounds; non relevant gains; propagationCoherence (statistics)Conditional probability distributiong-coherence checking; lower conditional probability bounds; non relevant gainsImprecise probabilityTheoretical Computer Sciencelower conditional probability boundRegular conditional probabilitynon relevant gainspropagationlower conditional probability boundsGeometry and Topologyg-coherence checkingSoftwareMathematics
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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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