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

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.