A synthesis of objective Bayesian and designed based methods for finite population sampling
Project Abstract
In the frequentist or design approach to finite population sampling prior information is incorporated in the sampling design. However in some cases when calculating estimates the design weights need to be readjusted, and then it can be difficult to find sensible estimates of variance. In the Bayesian approach prior information is incorporated through a prior distribution. Since the posterior distribution does not depend on the design it has been difficult to theoretically reconcile the two approaches. The Polya posterior is an objective Bayesian approach to finite population sampling that is appropriate when little or no prior information is available. The investigator is developing a synthesis of this objective Bayesian approach and the design based approach. It has two main threads. In the first the Polya posterior is extended to problems where it cannot be applied directly because of additional prior information contained in auxiliary variables. This leads to a constrained or restricted version of the Polya posterior. In the second Bayesian models are developed which directly include the design in the specification of the prior. Such models are a generalization of the Polya posterior and using them one can objectively incorporate into a prior the same kind of information that is encapsulated in a design. The investigator is developing the underlying theory and methods to simulate from these objective posteriors so that estimators can be found in practice and their frequentist properties studied.
One of the most basic problems of statistics is making an inference about a population based on a sample collected from the population. When little is known about the population the mean of the values in a random sample is used as an estimate of the population mean. However in addition to the estimate one also needs a sensible measure of its uncertainty or variance. In most situations there is prior information available about the population. This information should be used in deciding what units are to be included in the sample, the value of the estimate and the appropriate measure of uncertainty. The investigator is working on a synthesis of the two standard approaches to these problems. The results should make more effective use of available prior information than present methods. Because of the many surveys done each year by government and others improving survey practice is of great practical significance.
