A Gibbs sampler on the $n$-simplex

Abstract

We determine the mixing time of a simple Gibbs sampler on the unit simplex, confirming a conjecture of Aldous. The upper bound is based on a two-step coupling, where the first step is a simple contraction argument and the second step is a non-Markovian coupling. We also present a MCMC-based perfect sampling algorithm based on our proof which can be applied with Gibbs samplers that are harder to analyze.Comment: Published in at http://dx.doi.org/10.1214/12-AAP916 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org