Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques
Łatuszyński, Krzysztof, Miasojedow, Błażej and Niemiro, Wojciech (2011) Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2011 (No.2).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
The Nummellin’s split chain construction allows to decompose a Markov
chain Monte Carlo (MCMC) trajectory into i.i.d. "excursions". Regenerative MCMC
algorithms based on this technique use a random number of samples. They have
been proposed as a promising alternative to usual fixed length simulation [25, 33,
14]. In this note we derive nonasymptotic bounds on the mean square error (MSE)
of regenerative MCMC estimates via techniques of renewal theory and sequential
statistics. These results are applied to costruct confidence intervals. We then focus
on two cases of particular interest: chains satisfying the Doeblin condition and a geometric
drift condition. Available explicit nonasymptotic results are compared for
different schemes of MCMC simulation.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Monte Carlo method, Markov processes|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
1. Y.F. Atchade, F. Perron (2007): On the geometric ergodicity of Metropolis-Hastings algorithms.
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