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December 1998 Information bounds for Gibbs samplers
Priscilla E. Greenwood, Ian W. McKeague, Wolfgang Wefelmeyer
Ann. Statist. 26(6): 2128-2156 (December 1998). DOI: 10.1214/aos/1024691464

Abstract

If we wish to estimate efficiently the expectation of an arbitrary function on the basis of the output of a Gibbs sampler, which is better: deterministic or random sweep? In each case we calculate the asymptotic variance of the empirical estimator, the average of the function over the output, and determine the minimal asymptotic variance for estimators that use no information about the underlying distribution. The empirical estimator has noticeably smaller variance for deterministic sweep. The variance bound for random sweep is in general smaller than for deterministic sweep, but the two are equal if the target distribution is continuous. If the components of the target distribution are not strongly dependent, the empirical estimator is close to efficient under deterministic sweep, and its asymptotic variance approximately doubles under random sweep.

Citation

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Priscilla E. Greenwood. Ian W. McKeague. Wolfgang Wefelmeyer. "Information bounds for Gibbs samplers." Ann. Statist. 26 (6) 2128 - 2156, December 1998. https://doi.org/10.1214/aos/1024691464

Information

Published: December 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0927.62080
MathSciNet: MR1700224
Digital Object Identifier: 10.1214/aos/1024691464

Subjects:
Primary: 62G20, 62M05

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 1998
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