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Biometrika 1996 83(1):81-94; doi:10.1093/biomet/83.1.81
© 1996 by Biometrika Trust
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Rao-Blackwellisation of sampling schemes

GEORGE CASELLA and CHRISTIAN P. ROBERT

Biometrics Unit, Cornell University Ithaca, New York 14850, US.A.
Département de Mathématique CNRS-URA 1378, Université de Rouen, BP 118, 76134 Mont Saint-Aignan cedex, France

This paper proposes a post-simulation improvement for two common Monte Carlo methods, the Accept-Reject and Metropolis algorithms. The improvement is based on a Rao-Blackwellisation method that integrates over the uniform random variables involved in the algorithms, and thus post-processes the standard estimators. We show how the Rao-Blackwellised versions of these algorithms can be implemented and, through examples, illustrate the improvement in variance brought by these new procedures. We also compare the improved version of the Metropolis algorithm with ordinary and Rao-Blackwellised importance sampling procedures for independent and general Metropolis set-ups.

Key Words: Accept-reject • Gibbs sampling • Importance sampling • Metropolis • Monte Carlo algorithm • Polynomial computing time


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[Abstract] [PDF]


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