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Biometrika Advance Access originally published online on November 19, 2007
Biometrika 2007 94(4):992-998; doi:10.1093/biomet/asm065
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© 2007 Biometrika Trust

Miscellanea

Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications

Richard A. Lockhart

Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada lockhart{at}stat.sfu.ca

Federico J. O'Reilly

Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico federico{at}sigma.iimas.unam.mx

Michael A. Stephens

Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada stephens{at}stat.sfu.ca

Received for publication 1 March 2006. Revision received 1 March 2007.
  Abstract

A random sample is drawn from a distribution which admits a minimal sufficient statistic for the parameters. The Gibbs sampler is proposed to generate samples, called conditionally sufficient or co-sufficient samples, from the conditional distribution of the sample given its value of the sufficient statistic. The procedure is illustrated for the gamma distribution. Co-sufficient samples may be used to give exact tests of fit; for the gamma distribution these are compared for size and power with approximate tests based on the parametric bootstrap.

Key Words: Empirical distribution function test • Goodness-of-fit test • Parametric bootstrap • Rao–Blackwell • Sufficient statistic


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