Optimal Bayesian Design of Experiments for the One-Way Random Effects Model

Abstract

Since variance components are nonlinear parameters in a linear model, classical optimal designs for estimating variance components in the one-way random effects model depend on the values of the parameters. Optimal Bayesian designs are derived for the more realistic situation of unknown parameters, using the Fisher information of the variance components as a basis for comparing the designs. Balanced designs, in which the same number of measurements are taken on each unit, are shown to be optimal under various criteria for wide classes of priors in the one-way random effects model. In contrast to other nonlinear design problems, the number of support points for the design does not necessarily increase with increasingly vague prior information. Some design criteria that work well for other nonlinear design problems, such as D-optimality, do not give intuitively appealing designs for estimating variance components.