S. Moral Callejón
Credal sets are closed convex sets of probability measures. We will consider the problem of discounting a credal set when we have a value measuring our degree of confidence. The result will be a credal set which is less informative than the original one. For this aim, an axiomatic framework will be followed by determining the basic properties of this operation and providing several examples afterwards. The discounting of the convex hull of the union of two credal sets will be equal to the convex hull of the union of the discounting of the sets. So, to discount a credal set, it is enough to discount its extreme points. As a consequence we will concentrate in the problem of discounting of a single probability distribution. It is shown that the discounting has a strong relationship with divergence measures as Kullback-Leibler distance, but also considering other ones as Csiszar f-divergences. Two of the discounting operators will be interpreted in terms of gambles desirability.
Palabras clave / Keywords: imprecise probabilitiy, discounting, divergence measures, desirability
Programado
Sesión J01 Probabilidad y Aplicaciones
31 de mayo de 2018 09:00
Sala 4
