On the robustness of the predictive distribution for sampling from finite populations

Let [pi]N be the prior distribution on the number of items belonging to each of K([greater-or-equal, slanted]2) categories in a population of size N. It is shown that the marginal probability distribution of an ordered sample of items selected without replacement does not depend on N, provided the distributions {[pi]N} satisfy a simple relationship. This relationship holds for prior distributions in the multivariate Pólya-Eggenberger family. This distribution is also the same as that of an iid sample with the limit of [pi]N as prior. Thus one has non-dependence of the predictive distribution on the population size and one can quantify the sensitivity of the predictive to uncertainty about the prior.