Stochastic simulations conditioned on sufficient statistics

A general method for doing Monte Carlo simulations conditioned on sufficient statistics is presented. The basic idea is to adjust the parameter values in the corresponding unconditional simulation so that the actual value of the sufficient statistic is obtained. In the case of multiple solutions to this problem, the method has to be modified, even if the corresponding value of the simulated variable is unique for each-simulation. The methods are illustrated for some simple models in which the conditional distributions are well known. As a more complicated example, an exact 'analysis of variance' test in the gamma model is performed. Other examples are a modification of the Kolmogorov goodness-of-fit test into an exact test, and minimum variance unbiased estimation of cumulative distributions.