TY - CONF

T1 - On general conditional prevision assessments

AU - Sanfilippo, Giuseppe

PY - 2009

Y1 - 2009

N2 - 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 acharacterization 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.

AB - 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 acharacterization 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.

KW - Conditional events

KW - general conditional prevision assessments

KW - general conditional random quantities

KW - generalized Bayes Theorem

KW - generalized compound prevision theorem

KW - Conditional events

KW - general conditional prevision assessments

KW - general conditional random quantities

KW - generalized Bayes Theorem

KW - generalized compound prevision theorem

UR - http://hdl.handle.net/10447/47693

M3 - Other

SP - 23

EP - 34

ER -