SOME BAYESIAN AND NON-BAYESIAN PROCEDURES FOR THE ANALYSIS OF COMPARATIVE EXPERIMENTS AND FOR SMALL-AREA ESTIMATION - COMPUTATIONAL ASPECTS, FREQUENTIST PROPERTIES, AND RELATIONSHIPS

The estimation of a treatment contrast from experimental data and the estimation of a small-area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two-part mixed linear model. In this article a Bayesian approach to point and interval prediction is presented and its computational requirements are examined. Differences between the Bayesian approach and the traditional (classical) approach are discussed in general terms and, in addition, in terms of two examples taken from the literature: (1) the comparison of drug formulations in a biovailability trial (Westlake) and (2) the estimation of corn-crop areas using satellite data (Battese, Harter, and Fuller). Some deficiences in the classical approach are pointed out, and the Bayesian approach is considered from a frequentist perspective. It is shown, via a Monte Carlo study, that, for certain (noninformative) choices of the prior distribution, the frequentist properties of the Bayesian prediction procedures compare favorably with those of their classical counterparts and that, in certain situations, they produce different and more sensible answers.