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

Abstract

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.Finite population Hypergeometric Limit distribution Multinomial Multivariate Multivariate hypergeometric Polya urn model Polya-Eggenberger distributions Predictive distribution Sampling distribution Sampling without replacement