Bayesian optimal experimental design for treatment—control comparisons in the presence of two-way heterogeneity

Abstract

Optimal Bayesian experimental design is derived for the one-way analysis of variance in the presence of two-way heterogeneity. The design is optimal for the estimation of the treatment-control contrasts, minimizing their posterior expected squared error loss. The prior knowledge of the treatment and blocking effects is modelled by Normal distribution, the treatments being exchangeable. A method for the derivation of the optimal design for any covariance structure of the blocking effects is given. For a special interesting covariance matrix of the blocking effects, the optimal design is derived.