6533b855fe1ef96bd12aff67
RESEARCH PRODUCT
Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence
Angelo GilioGiuseppe Sanfilipposubject
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)Mathematicsdescription
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 conditional cannot formalize Bayesian updating but has an economic rationale. Finally, we define the coherence for prevision assessments on iterated c.r.q.’s and we give an illustrative example.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |