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arXiv · 1107.5829

A Gibbs sampler on the $n$-simplex

Aaron Smith
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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.

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Aaron Smith. 2011-07-28. A Gibbs sampler on the $n$-simplex. https://doi.org/10.1214/12-aap916

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