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Error bounds for computing the expectation by Markov chain Monte Carlo

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  • Rudolf Daniel

    (Friedrich Schiller University Jena, Mathem. Institute, Ernst-Abbe-Platz 2, D-07743 Jena, Germany. E-mail:)

Abstract

We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l 2-, l 4- and l ∞-norm of the function are proven. By the estimation the well-known asymptotical limit of the error is attained, i.e. our bounds are correct to first order as n → ∞. We discuss the dependence of the error on a burn-in of the Markov chain. Furthermore we suggest and justify a specific burn-in for optimizing the algorithm.

Suggested Citation

  • Rudolf Daniel, 2010. "Error bounds for computing the expectation by Markov chain Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 323-342, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:323-342:n:5
    DOI: 10.1515/mcma.2010.012
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    References listed on IDEAS

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    1. Federico Bassetti & Fabrizio Leisen, 2007. "Metropolis Algorithm and equienergy sampling for two mean field spin systems," Economics and Quantitative Methods qf0704, Department of Economics, University of Insubria.
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