Error bounds for computing the expectation by Markov chain Monte Carlo

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

Monte Carlo Methods and Applications, 2010, vol. 16, issue 3-4, 323-342

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 l2-, l4- 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.

Keywords: Markov chain Monte Carlo methods; Markov chain Monte Carlo; error bounds; explicit error bounds; burn-in; mixing time; eigenvalue (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/mcma.2010.012

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