
TL;DR
This paper analyzes the mixing time of a Gibbs sampler on the n-simplex, confirming Aldous's conjecture, and introduces a perfect sampling algorithm based on their proof for more complex Gibbs samplers.
Contribution
It provides a rigorous determination of the mixing time for a Gibbs sampler on the n-simplex and presents a novel perfect sampling algorithm applicable to complex cases.
Findings
Confirmed Aldous's conjecture on mixing time.
Developed a two-step coupling method for analysis.
Proposed a MCMC-based perfect sampling algorithm.
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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