Search results for " Conditional previsions"

showing 2 items of 2 documents

Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence

2013

We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH c , where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y|K coincide. We show that X|HK coincides with a suitable c.r.q. Y|K and we apply this representation to Bayesian updating of probabilities, by also deepening some aspects of Bayes’ formula. Then, we introduce a notion of iterated c.r.q. (X|H)|K, by analyzing its relationship with X|HK. Our notion of iterated conditiona…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaSettore INF/01 - Informaticaconditional random quantitiesCoherence (statistics)Bayesian inferencebayesian updatingcoherenceCombinatoricsconditional previsionsBayes' theoremIterated functionbayesian updating; conditional random quantities; betting scheme; conditional previsions; coherence; iterated conditioning; iterated conditioning.Coherence betting scheme conditional random quantities conditional previsions Bayesian updating iterated conditioning.Scheme (mathematics)iterated conditioningConditioningRepresentation (mathematics)betting schemeEvent (probability theory)Mathematics
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Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities

2022

We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for …

Settore MAT/06 - Probabilita' E Statistica MatematicaCoherence Conditional events Conditional random quantities Conditional previsions Conjoined and disjoined conditionals Iterated conditionals Compound probability theorem Lower and upper bounds Import-export principle
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