Bayesian Predictive Inference For Finite Population Quantities Under Informative Sampling

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection probabilities corresponding to the sample units are known. Our methodology, unlike that of Chambers, Dorfman and Wang (1998), can be used to make inference for finite population quantities and provides measures of precision and intervals. Moreover, our methodology, using Markov chain Monte Carlo methods, avoids the necessity of using asymptotic closed form approximations, necessary for the other approaches that have been proposed. A set of simulated examples shows that the informative model provides improved precision over a standard ignorable model, and corrects for the selection bias.