Sharp Total Variation Bounds for Finitely Exchangeable Arrays

TL;DR

This paper explores the connection between finitely exchangeable arrays and sequences, providing precise bounds on how close their distributions are in total variation distance, which advances understanding in exchangeability theory.

Contribution

It introduces sharp bounds on total variation distance between finitely and infinitely exchangeable arrays, clarifying their relationship.

Findings

Derived explicit bounds on total variation distance

Established the relationship between array and sequence exchangeability

Provided theoretical insights into exchangeability approximations

Abstract

In this article we demonstrate the relationship between finitely exchangeable arrays and finitely exchangeable sequences. We then derive sharp bounds on the total variation distance between distributions of finitely and infinitely exchangeable arrays.