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RESEARCH PRODUCT
On general conditional prevision assessments
V. BiazzoAngelo GilioG. Sanfilipposubject
Conditional random quantities; coherence; conditional prevision assessments; random gain; alternative theorems; algorithms; imprecise assessments; generalized and total coherence.Settore MAT/06 - Probabilita' E Statistica Matematicarandom gainConditional events general conditional random quantitiesgeneral conditional prevision assessments generalized compound prevision theorem generalized Bayes TheoremConditional random quantitiesalgorithmsimprecise assessmentsalternative theoremsgeneralized and total coherencecoherenceconditional prevision assessmentsdescription
In this paper we consider general conditional random quantities of the kind $X|Y$, where $X$ and $Y$ are finite discrete random quantities. Then, we introduce the notion of coherence for conditional prevision assessments on finite families of general conditional random quantities. Moreover, we give a compound prevision theorem and we examine the relation between the previsions of $X|Y$ and $Y|X$. Then, we give some results on random gains and, by a suitable alternative theorem, we obtain a characterization of coherence. We also propose an algorithm for the checking of coherence. Finally, we briefly examine the case of imprecise conditional prevision assessments by introducing the notions of generalized and total coherence. To illustrate our results, we consider some examples.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 |