Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data

Abstract

Motivated by de Finetti’s representation theorem for almost exchangeable arrays, we want to sample p∈[0,1]d from a distribution with density proportional to exp(−A2∑i<jcij(pi−pj)2), where A is large and cij’s are non-negative weights. We analyze the rate of convergence of a coordinate Gibbs sampler used to simulate from these measures. We show that for every non-zero fixed matrix C=(cij), and large enough A, mixing happens in Θ(A2) steps in a suitable Wasserstein distance. The upper and lower bounds are explicit and depend on the matrix C through few relevant spectral parameters.