Electronic Journal of Statistics

Construction of weakly CUD sequences for MCMC sampling

Seth D. Tribble and Art B. Owen

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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.

Article information

Electron. J. Statist., Volume 2 (2008), 634-660.

First available in Project Euclid: 30 July 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 11K45: Pseudo-random numbers; Monte Carlo methods 11K41: Continuous, $p$-adic and abstract analogues

completely uniformly distributed Gibbs sampler equidistribution probit quasi-Monte Carlo


Tribble, Seth D.; Owen, Art B. Construction of weakly CUD sequences for MCMC sampling. Electron. J. Statist. 2 (2008), 634--660. doi:10.1214/07-EJS162. https://projecteuclid.org/euclid.ejs/1217450798

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