Construction of weakly CUD sequences for MCMC sampling

Details Construction of weakly CUD sequences for MCMC sampling Construction of weakly CUD sequences for MCMC sampling

2008-07-30

arxiv.org/abs/0807.4858v1

Electronic Journal of Statistics 2008, Vol. 2, 634-660

Statistics

Computation

Published in at http://dx.doi.org/10.1214/07-EJS162 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

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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