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

Sudip Bose

Statistics & Probability Letters, 2004, vol. 69, issue 1, 21-27

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.

Keywords: Finite; population; Hypergeometric; Limit; distribution; Multinomial; Multivariate; Multivariate; hypergeometric; Polya; urn; model; Polya-Eggenberger; distributions; Predictive; distribution; Sampling; distribution; Sampling; without; replacement (search for similar items in EconPapers)
Date: 2004
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