Explicit error bounds for lazy reversible Markov chain Monte Carlo

  • Authors:

  • Daniel Rudolf

  • Affiliations:

  • Friedrich Schiller University Jena, Mathem. Institute, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

  • Venue:
  • Journal of Complexity
  • Year:
  • 2009

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Abstract

We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure @p which can be given by a density @r with respect to another measure. A straight simulation of the desired distribution by a random number generator is in general not possible. Thus it is reasonable to use Markov chain sampling with a burn-in. We study such an algorithm and extend the analysis of Lovasz and Simonovits [L. Lovasz, M. Simonovits, Random walks in a convex body and an improved volume algorithm, Random Structures Algorithms 4 (4) (1993) 359-412] to obtain an explicit error bound.