Bayesian Optimization in Sampling Finite Populations

Abstract The problem of optimum allocation in sampling finite populations using prior information is considered. The following cases are investigated: (1) stratified simple random sampling with known strata sizes; (2) Neyman's double sampling with unknown strata sizes; (3) the Hansen-Hurwitz method for the non-response problem; (4) two-stage random sampling. The optimum allocation in each case is obtained by minimizing the expected posterior variance of the mean subject to constraints. The results are extended to multiple prior distributions and/or multiple characters. The solutions are distribution-free and also free from the assumption of infinite populations and/or known variances. Attention is given to “data-based” prior distributions.