Explicit error bounds for lazy reversible Markov Chain Monte Carlo
Numerical Analysis
2011-01-18 v2 Probability
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.
Cite
@article{arxiv.0805.3587,
title = {Explicit error bounds for lazy reversible Markov Chain Monte Carlo},
author = {Daniel Rudolf},
journal= {arXiv preprint arXiv:0805.3587},
year = {2011}
}