Positive Dependence of Exchangeable Sequences

Abstract

AbstractInfinite sequences of exchangeable binary random variables have strong positive dependence properties; in particular, we show they are strong FKG. If the infinite exchangeable sequence is allowed to have multiple values this is no longer true. Positive dependence conditions such as association still have natural application in this context. We establish necessary and sufficient conditions for an infinite exchangeable sequence to be associated. This result shows that exchangeable Polyà urn processes are associated. We also establish necessary and sufficient conditions for finite exchangeable sequences to be weakly associated. The match set distribution of a random permutation has recently been shown to be associated by an extensive analysis of cases. Our result easily yields the weak association of such distributions.