Bayesian Estimation of the Size of a Population

We consider the following problem: estimate the size of a
population marked with serial numbers after only a sample of the
serial numbers has been observed. Its simplicity in formulation and
the inviting possibilities of application make this estimation well
suited for an undergraduate level probability course. Our
contribution consists in a Bayesian treatment of the problem. For
an improper uniform prior distribution, we show that the posterior
mean and variance have nice closed form expressions and we
demonstrate how to compute highest posterior density intervals.
Maple and R code is provided on the authors’ web-page to allow
students to verify the theoretical results and experiment with
data.