Finite population sampling as a prediction problem

The Bayesian approach to finite population sampling makes statistical inference into a prediction problem in a very natural way. The Polya posterior yields a noninformative Bayesian approach when little or no prior information is available. In addition to the characteristic of interest, related auxiliary variables are often present. The Polya posterior can be extended to handle some of these cases. This is done by restricting the Polya posterior so that given a sample, simulated copies of the entire population can be generated which satisfy the constraints induced by the prior information. Inferences or predictions can then be made using this restricted or constrained Polya posterior.