Search results for "Regular conditional probability"

showing 5 items of 5 documents

Radon transform as a set of probability distributions

2009

It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.

Integral transformsOptical tomographySettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciRadon transformCharacteristic function (probability theory)Mathematical analysisWigner semicircle distributionCondensed Matter PhysicsConvolution of probability distributionsAtomic and Molecular Physics and OpticsSettore FIS/03 - Fisica Della MateriaRegular conditional probabilityProbability distributionWigner distribution functionQuantum tomographyMathematical PhysicsMathematicsK-distribution
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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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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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Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework

2004

Regular conditional probabilitySurvival probabilityJoint probability distributionApplied MathematicsProbability mass functionCalculusRelaxation (physics)Probability distributionStatistical physicsDiffusion (business)MathematicsProbability measureApplicationes Mathematicae
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Conjunction, Disjunction and Iterated Conditioning of Conditional Events

2013

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the…

Theoretical computer scienceSettore MAT/06 - Probabilita' E Statistica MatematicaComputer scienceProbabilistic logicCoherence (philosophical gambling strategy)Conditional events conditional random quantities conjunction disjunction iterated conditionalsConjunction (grammar)Set (abstract data type)Regular conditional probabilitydisjunction; conditional events; conjunction; conditional random quantities; iterated conditionals.Iterated functionRepresentation (mathematics)Settore SECS-S/01 - StatisticaMathematical economicsEvent (probability theory)
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