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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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
Official Date:	2011
Dates:	Date Event 2011 Published
Volume:	Vol.2011
Number:	No.2
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access

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