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April 2011 Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
S. Chen, J. Dick, A. B. Owen
Ann. Statist. 39(2): 673-701 (April 2011). DOI: 10.1214/10-AOS831

Abstract

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than i.i.d. U(0, 1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.

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S. Chen. J. Dick. A. B. Owen. "Consistency of Markov chain quasi-Monte Carlo on continuous state spaces." Ann. Statist. 39 (2) 673 - 701, April 2011. https://doi.org/10.1214/10-AOS831

Information

Published: April 2011
First available in Project Euclid: 9 March 2011

zbMATH: 1225.65010
MathSciNet: MR2816335
Digital Object Identifier: 10.1214/10-AOS831

Subjects:
Primary: 62F15 , 65C40
Secondary: 26A42 , 65C05

Keywords: Completely uniformly distributed , coupling , iterated function mappings , Markov chain Monte Carlo

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • April 2011
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