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arXiv · 1106.4739

Nonasymptotic bounds on the estimation error of MCMC algorithms

Krzysztof Łatuszyński·Błażej Miasojedow·Wojciech Niemiro
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Abstract

We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is nonasymptotic. 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 $σ_{\mathrm {as}}^2(P,f)/n$, where $σ_{\mathrm{as}}^2(P,f)$ is the CLT asymptotic variance. Next, we proceed to specific additional assumptions and give explicit computable bounds for geometrically and polynomially ergodic Markov chains under quantitative drift conditions. As a corollary, we provide results on confidence estimation.

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Krzysztof Łatuszyński, Błażej Miasojedow, Wojciech Niemiro. 2013-12-11. Nonasymptotic bounds on the estimation error of MCMC algorithms. https://doi.org/10.3150/12-bej442

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