Contributions to Bayesian optimization in sampling and sampling in time

Abstract

The problem of optimum allocation of a sample in stratified and two-stage sampling is considered from Bayesian viewpoint by minimizing prior expectation of the posterior variance of the population mean. For the non-response problem optimum allocations are obtained for the initial sample size and the sample size for the non-respondents by using extensive form of analysis. The loss function used is linear in the costs and prior expectation of the posterior variance. For sampling on two occasions from a finite population Kulldorff's composite regression estimator for the population total on the second occasion is shown to be more efficient than Pathak and Rao's composite regression estimator assuming equal expected costs. An analogous result is proved for composite difference estimators. The method of random stratification of Rao, Hartley and Cochran is applied to probability proportional to size sampling on two occasions and a composite difference estimator is suggested. This estimator is shown to be often more efficient than that of Des Raj. A similar composite difference estimator is suggested for the method of inclusion probability proportional to size and its efficiency as compared to the estimator based on sampling on one occasion is determined.