BAYESIAN OPTIMAL DESIGNS FOR LINEAR-REGRESSION MODELS

A Bayesian version of Elfving's theorem is given for the c-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian c-optimum are described. The class of prior precision matrices R for which the Bayesian c-optimal designs are supported by the points of the classical c-optimal design is characterized. It is proved that the Bayesian c-optimal design, for large n, is always supported by the same support points as the classical one if the number of support points and the number of regression functions are equal. Examples and a matrix analog are discussed.