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Nonasymptotic bounds on the estimation error of MCMC algorithms
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Łatuszyński, Krzysztof, Miasojedow, Blazej and Niemiro, Wojciech (2013) Nonasymptotic bounds on the estimation error of MCMC algorithms. Bernoulli, Volume 19 (Number 5a). pp. 2033-2066. doi:10.3150/12-BEJ442 ISSN 1350-7265.
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Official URL: http://dx.doi.org/10.3150/12-BEJ442
Abstract
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 �2 as(P; f)=n, where �2
as(P; f) 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.
Item Type: | Journal Article | ||||
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Alternative Title: | |||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Bernoulli | ||||
Publisher: | Int Statistical Institute | ||||
ISSN: | 1350-7265 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 19 | ||||
Number: | Number 5a | ||||
Page Range: | pp. 2033-2066 | ||||
DOI: | 10.3150/12-BEJ442 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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