Path coupling without contraction

13 years 4 months ago

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Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than deﬁning and analysing the coupling on every pair in Ω×Ω, where Ω is the state space of the Markov chain, analysis is done on a smaller set S ⊆ Ω × Ω. If the coeﬃcient of contraction β is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if β = 1 then analysis (of the variance) is still required for all pairs in Ω × Ω. In this paper we present a new approach which shows rapid mixing in the case β = 1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved. We also present a technique applicable when β = 1 and our condition is not met. Key words: Markov chain, Markov chain Monte Carlo, Path coupling, coupling

Magnus Bordewich, Martin E. Dyer

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