Search results for "bayesian updating"

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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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