Distorted Probabilities and Bayesian Confirmation Measures

Bayesian Confirmation Measures (BCMs) assess the impact of the occurrence of one event on the credibility of another. Many mea- sures of this kind have been defined in literature. We want to analyze how these measures change when the probabilities involved in their computation are distorted. Composing distortions and BCMs we define a set of Distorted Bayesian Confirmation Measures (DBCMs); we study the properties that DBCMs may inherit from BCMs, and propose a way to measure the degree of distortion of a DBCM with respect to a corre- sponding BCM.