Explicit error bounds for lazy reversible Markov Chain Monte Carlo

TL;DR

This paper derives explicit, non-asymptotic error bounds for Markov Chain Monte Carlo methods, providing practical guarantees for the accuracy of expectation estimates in sampling algorithms like Metropolis.

Contribution

It extends previous analyses to establish concrete error bounds for MCMC methods, including burn-in considerations, for the first time in a non-asymptotic setting.

Findings

Provides explicit error bounds for MCMC algorithms.

Extends Lovasz and Simonovits' analysis to practical sampling.

Offers theoretical guarantees for expectation estimation accuracy.

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 which can be given by a density 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 (1993) to obtain an explicit error bound.