Balanced samples and robust Bayesian inference in finite population sampling

Abstract

SUMMARY Bayesian inference in finite populations uses probability models at two stages: (i) to describe relationships among population units and (ii) to express uncertainty concerning the values of parameters appearing at stage (i). Here we consider the Bayes posterior distribution of the population total when a multivariate normal regression model is used at stage (i), with a diffuse prior distribution on the regression coefficients. We study the situation where the stage (i) model is in error because an important regressor is omitted, and we show that in balanced samples such errors do not affect the posterior distribution. Cases where the covariance matrix contains an unknown scale parameter or is itself misspecified are also considered.