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Paper No. 11-04

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KG Latuszynski and GO Roberts

CLTs and asymptotic variance of time-sampled Markov chains

Date: February 2011

Abstract: For a Markov transition kernel P and a probability distribution on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel P_ = P k _(k)Pk: In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance. AMS 2000 subject classi_cations: Primary 60J05, 65C05.

Keywords: Time-sampled Markov chains, Barker's algorithm, Metropolis algorithm, Central Limit Theorem, asymptotic variance, variance bounding Markov chains, MCMC estimation.