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.
© de Gruyter 2010