Variance reduction in gibbs sampler using quasi random numbers

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A sequence of s-dimensional quasi random numbers fills the unit cube evenly at a much faster rate than a sequence of pseudo uniform deviates does. It has been successfully used in many Monte Carlo problems to speed up the convergence. Direct use of a sequence of quasi random numbers, however, does not work in Gibbs samplers because the successive draws are now dependent. We develop a quasi random Gibbs algorithm in which a randomly permuted quasi random sequence is used in place of a sequence of pseudo deviates. One layer of unnecessary variation in the Gibbs sample is eliminated. A simulation study with three examples shows that the proposed quasi random algorithm provides much tighter estimates of the quantiles of the stationary distribution and is about 4–25 times as efficient as the pseudo algorithm. No rigorous theoretical justification for the quasi random algorithm, however, is available at this point.

Original languageEnglish (US)
Pages (from-to)253-266
Number of pages14
JournalJournal of Computational and Graphical Statistics
Volume7
Issue number3
DOIs
StatePublished - Jan 1 1998

Fingerprint

Variance Reduction
Gibbs Sampler
Random number
Unit cube
Random Sequence
Stationary Distribution
Quantile
Justification
Speedup
Simulation Study
Gibbs sampler
Variance reduction
Dependent
Estimate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics

Cite this

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Variance reduction in gibbs sampler using quasi random numbers. / Liao, Jiangang (Jason).

In: Journal of Computational and Graphical Statistics, Vol. 7, No. 3, 01.01.1998, p. 253-266.

Research output: Contribution to journalArticle

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