Discovery Sampling and Selection Models

Various aspects of Bayesian inference in selection and size biased sampling problems are presented beginning with discussion of general problems of inference in in nite and nite populations subject to selection sampling Estimation of the size of nite populations and inference about superpopulation distributions when sampling is apparently informative is then developed in two speci c problems The rst is a simple example of truncated data analysis and some details of simulation based Bayesian analysis are presented The sec ond concerns discovery sampling in which units of a nite population are selected with probabilities proportional to some measure of size A well known area of application is in the discovery of oil reserves and some recently published data from this area is analysed here Solutions to the computational problems arising are developed using iterative simula tion methods Finally some comments are made on extensions including multiparameter superpopulations semi parametric models and problems of dealing with missing data in discovery sampling