Search results for "iterated conditioning"

showing 3 items of 3 documents

Conditional Random Quantities and Compounds of Conditionals

2013

In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a conditional event $E|H$ is looked at as a three-valued quantity with values 1, or 0, or $p$, where $p$ is the probability of $E|H$. We introduce a notion of iterated conditional random quantity of the form $(X|H)|K$ defined as a suitable conditional random quantity, which coincides with $X|HK$ when $H \subseteq K$. Based on 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 cohere…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaLogicImport–Export principleProbability (math.PR)Probabilistic logicConjunctionOf the formSettore M-FIL/02 - Logica E Filosofia Della ScienzaCoherence (philosophical gambling strategy)Conditional random quantitieConjunction (grammar)Lower/upper prevision boundsHistory and Philosophy of ScienceNegationIterated functionIterated conditioningFOS: MathematicsConditional eventRepresentation (mathematics)CoherenceDisjunctionMathematics - ProbabilityMathematicsEvent (probability theory)
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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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On general conditional random quantities

2009

In the first part of this paper, recalling a general discussion on iterated conditioning given by de Finetti in the appendix of his book, vol. 2, we give a representation of a conditional random quantity $X|HK$ as $(X|H)|K$. In this way, we obtain the classical formula $\pr{(XH|K)} =\pr{(X|HK)P(H|K)}$, by simply using linearity of prevision. Then, we consider the notion of general conditional prevision $\pr(X|Y)$, where $X$ and $Y$ are two random quantities, introduced in 1990 in a paper by Lad and Dickey. After recalling the case where $Y$ is an event, we consider the case of discrete finite random quantities and we make some critical comments and examples. We give a notion of coherence fo…

Settore MAT/06 - Probabilita' E Statistica Matematicageneral conditional random quantities; general conditional prevision assessments; generalized compound prevision theoremgeneral conditional prevision assessmentsiterated conditioninggeneralized compound prevision theoremgeneral conditional random quantitiesconditional eventsstrong generalized compound prevision theoremConditional events general conditional random quantities general conditional prevision assessments generalized compound prevision theorem iterated conditioning strong generalized compound prevision theoremconditional events; general conditional random quantities; general conditional prevision assessments; generalized compound prevision theorem; iterated conditioning; strong generalized compound prevision theorem.
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