Irrelevance and independence axioms in Quasi-Bayesian theory

Abstract

This paper investigates Walley’s concepts of irrelevance and independence, as applied to the theory of closed convex sets of probability measures. Walley’s concepts are analyzed from the perspective of axioms for conditional independence (the so-called semi-graphoid axioms). Two new results are demonstrated in discrete models: rst, Walley’s concept of irrelevance is an asymmetric semi-graphoid; second, Walley’s concept of independence is an incomplete semi-graphoid. These results are the basis for an understanding of irrelevance and independence in connection to the theory of closed convex sets of probability measures, a theory that has received attention as a powerful representation for uncertainty in beliefs and preferences.