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Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques
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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).

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Abstract
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 
Date:  2011 
Volume:  Vol.2011 
Number:  No.2 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/34871 
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