Rationale and properties of the intersection probability

In this paper we analyze the properties of the intersection probability, a recent Bayesian transformation of belief functions introduced by geometric means. We propose a rationale for this approximation valid for interval probabilities, and study its geometry in the probability simplex with respect to the credal sets associated with probability intervals. We discuss its relations with different evidence combination rules and the affine combination operator. We conclude by running an analytical comparison between the intersection probability and other probability transformations of the so-called “affine” family.