Bayesian Inference for Finite Population Parameters in Multistage Cluster Sampling

Assuming a model appropriate for many multistage sample surveys, Bayesian predictive inference for a general linear function, ω, of the finite population elements is described. In a broad class of linear estimators of ω, the posterior mean, E″(ω), of ω is shown to have the optimal frequentist property of minimal bounded mean squared error. For the special case of three-stage sampling, E″(ω) is described in detail. Also presented are the results of an investigation of the effect on inferences of alteration of the values of some parameters in the prior distribution.