Bayesian Estimation of the Size of a Population

Maple and R code for the "Bayesian Estimation of the Size of a Population" article by M. Höhle and L. Held (2005).

Abstract:
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 problem well suited for an undergraduate level probability course. Our contribution consists in a Bayesian treatment of this estimation problem. We show that the posterior mean and variance have nice closed form expressions for an improper uniform prior distribution and 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 real data.

• The Maple Worksheet bayespopsize.mws

• The R file bayespopsize.R containing code to compute posterior mean and variance directly and by an approximative method. The function munster as example generates the graphics used for the Munster Bank example.
  
• The two support files hypergeometric.R and plottools.R are needed.