Error bounds for computing the expectation by Markov chain Monte Carlo

Abstract

We study the error of reversible Markov chain Monte Carlo methods for approx-imating the expectation of a function. Explicit error bounds with respect to thel2-,l4-andl1-norm of the function are proven. By the estimation the well-known asymptotical limitof the error is attained, i.e. our bounds are correct to first order asn!1. We discuss thedependence of the error on a burn-in of the Markov chain. Furthermore we suggest andjustify a specific burn-in for optimizing the algorithm.