This paper introduces a hierarchical Bayes (HB) approach for prediction in general mixed linear models. The results find application in small area estimation. Our model unifies and extends a number of models previously considered in this area. Computational formulas for obtaining the Bayes predictors and their standard errors are given in the general case. The methods are applied to two actual data sets. Also, in a special case, the HB predictors are shown to possess some interesting frequentist properties.
"Bayesian Prediction in Linear Models: Applications to Small Area Estimation." Ann. Statist. 19 (4) 1748 - 1770, December, 1991. https://doi.org/10.1214/aos/1176348369