Bayes D-optimal and E-optimal block designs

Abstract

Bayes designs are considered for a two-way analysis of variance model with a normal prior for treatments and blocks, one of the treatments acting as a control. The existence of an optimal allocation is proved for each Bayesian optimality criterion, i.e. each criterion defined on the posterior covariance matrix for the treatments. Under a special assumption on the treatment prior, the structure of the optimal design is specified; for the case of only one test treatment such a design is universally optimal. Bayes D- and E- optimal designs are found as special cases and results are compared with classical ones. Two examples are included.