A new look at inference for the Hypergeometric Distribution

The problem of inference for the proportion of successes in a finite populations is given much less attention in both inference and application courses than the related infinite population problem. However, the finite population problem is both interesting and useful in its own right while also providing insight into various approaches for the infinite population case. This article explores exact Bayesian inferences for understanding a finite population proportion. The derivations of both posterior and posterior predictive distributions provide excellent insight for students regarding the updating nature of the Bayesian paradigm. The novel approach presented for deriving the posterior predictive distribution also allows students to overcome difficult combinatorial calculations. Accessible limiting arguments also can be used to justify the use of flat priors in the infinite populations. Finally , the results may be compared to conventional inferences based upon the use of finite population correction factors or exact frequentist intervals.