Inference in Successive Sampling Discovery

A variety of practical problems of nite population inference can be addressed in the framework of successive sampling discovery models { population units are assumed drawn from a superpopulation distribution and then successively sampled according to a speciied`size-biased' selection mechanism. Formal statistical analysis of discovery data under such models is technically challenging, as exempliied by the likelihood analyses of Nair and Wang (1989). Assessment of uncertainties about superpopulation parameters and, more critically, appropriate forms of predictive inference for the unsampled units in the nite population, are open issues that are addressed here from a Bayesian perspective. Motivated by the likelihood analysis of Nair and Wang (1989), we develop a formal Bayesian approach to analysis in the same class of models; we show how simulation methods provide for the computation of required posterior and predictive distributions of relevance. We further develop model extensions to cover problems of uncertainty about nite population sizes, uncertainty about sample selection mechanisms, and other practical issues. Several analyses of the oil reserve data of Nair and Wang (1989) are used for illustration.