Bayesian Methods for Finite Population Sampling

The present monograph is primarily an outgrowth of our own re­ search on certain aspects of Bayesian inference in finite population sampling. Finite population sampling has been an integral part of statistics since its beginning. The topic continues its impact in the theory and practice of statistics, especially for researchers in survey sampling. Inference for finite population sampling utilizes prior information either explicitly or implicitly. Bayesian inference makes explicit use of this information as part of the model. This is in striking con­ trast to design- based inference in survey sampling where prior knowledge is incorporated only as auxiliary information. On the other hand there is a elose relationship between the Bayesian ap­ proach and the superpopulation approach, although they differ in their foundational interpretations. Operationally, however, the dif­ ference is much less pronounced as many estimators obtained via superpopulation models are also obtainable as Bayes estimators, and vice versa. This monograph, does not aim to provide a complete up-to-date account of the Bayesian literature in finite population sampling. Rather, it treats the topics reflecting the authors' personal inter­ ests. Its main aim is to demonstrate that a variety of levels of prior information can be used in survey sampling in a Bayesian man­ ner. Situations considered range from a noninformative Bayesian justification of standard frequentist methods when the only prior information available is the belief in the exchangeablility of the units to a full-fledged Bayesian model.