CLTs and Asymptotic Variance of Time-Sampled Markov Chains

Krzysztof Łatuszyński () and Gareth O. Roberts
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Krzysztof Łatuszyński: University of Warwick
Gareth O. Roberts: University of Warwick

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 1, 237-247

Abstract: Abstract For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\mu} = \sum_k \mu(k)P^k.$ 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.

Keywords: Time-sampled Markov chains; Barker’s algorithm; Metropolis algorithm; Central Limit Theorem; Asymptotic variance; Variance bounding Markov chains; MCMC estimation; 60J05; 60F05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9237-8

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