Bayesian $T$-optimal discriminating designs

Abstract

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally $T$-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved, and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail.