Nonasymptotic bounds on the estimation error of MCMC algorithms

Details Nonasymptotic bounds on the estimation error of MCMC algorithms Nonasymptotic bounds on the estimation error of MCMC algorithms

2011-06-23

arxiv.org/abs/1106.4739v2

Statistics

Methodology

36 pages, supersedes arXiv:0907.4915, to appear in Bernoulli

Scientific paper

We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is non-asymptotic. We first establish a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a possibly unbounded target function $f.$ The bound is sharp in the sense that the leading term is exactly $\asvar/n$, where $\asvar$ is the CLT asymptotic variance. Next, we proceed to specific assumptions and give explicit computable bounds for geometrically and polynomially ergodic Markov chains. As a corollary we provide results on confidence estimation.

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