Accessible Requires Authentication Published by De Gruyter October 20, 2010

Error bounds for computing the expectation by Markov chain Monte Carlo

Daniel Rudolf
From the journal

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.

Received: 2009-09-25
Revised: 2010-09-08
Published Online: 2010-10-20
Published in Print: 2010-December

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