Open Access
2008 Construction of weakly CUD sequences for MCMC sampling
Seth D. Tribble, Art B. Owen
Electron. J. Statist. 2: 634-660 (2008). DOI: 10.1214/07-EJS162


In Markov chain Monte Carlo (MCMC) sampling considerable thought goes into constructing random transitions. But those transitions are almost always driven by a simulated IID sequence. Recently it has been shown that replacing an IID sequence by a weakly completely uniformly distributed (WCUD) sequence leads to consistent estimation in finite state spaces. Unfortunately, few WCUD sequences are known. This paper gives general methods for proving that a sequence is WCUD, shows that some specific sequences are WCUD, and shows that certain operations on WCUD sequences yield new WCUD sequences. A numerical example on a 42 dimensional continuous Gibbs sampler found that some WCUD inputs sequences produced variance reductions ranging from tens to hundreds for posterior means of the parameters, compared to IID inputs.


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Seth D. Tribble. Art B. Owen. "Construction of weakly CUD sequences for MCMC sampling." Electron. J. Statist. 2 634 - 660, 2008.


Published: 2008
First available in Project Euclid: 30 July 2008

zbMATH: 1320.62055
MathSciNet: MR2426105
Digital Object Identifier: 10.1214/07-EJS162

Primary: 62F15
Secondary: 11K41 , 11K45

Keywords: Completely uniformly distributed , equidistribution , Gibbs sampler , probit , quasi-Monte Carlo

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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