### 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 language | English (US) |
---|---|

Pages (from-to) | 253-266 |

Number of pages | 14 |

Journal | Journal of Computational and Graphical Statistics |

Volume | 7 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1998 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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**Variance reduction in gibbs sampler using quasi random numbers.** / Liao, J. G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Variance reduction in gibbs sampler using quasi random numbers

AU - Liao, J. G.

PY - 1998/9

Y1 - 1998/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032363290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032363290&partnerID=8YFLogxK

U2 - 10.1080/10618600.1998.10474775

DO - 10.1080/10618600.1998.10474775

M3 - Article

AN - SCOPUS:0032363290

VL - 7

SP - 253

EP - 266

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 3

ER -