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CLTs and Asymptotic Variance of Time-Sampled Markov Chains

Author

Listed:
  • Krzysztof Łatuszyński

    (University of Warwick)

  • Gareth O. Roberts

    (University of Warwick)

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.

Suggested Citation

  • Krzysztof Łatuszyński & Gareth O. Roberts, 2013. "CLTs and Asymptotic Variance of Time-Sampled Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 237-247, March.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:1:d:10.1007_s11009-011-9237-8
    DOI: 10.1007/s11009-011-9237-8
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    References listed on IDEAS

    as
    1. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    2. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "A Factorisation of Diffusion Measure and Finite Sample Path Constructions," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 85-104, March.
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