title: BayesianT-optimal discriminating designs.
abstract: The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to theT-optimality criterion introduced by Atkinson and Fedorov (1975a) is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locallyT-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.
authors.affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany, holger.dette@rub.de.
authors.forename: Holger
authors.initials: H
authors.lastname: Dette
authors.affiliation: St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia, vbmelas@post.ru.
authors.forename: Viatcheslav B
authors.initials: VB
authors.lastname: Melas
authors.affiliation: St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia, romanguchenko@ya.ru.
authors.forename: Roman
authors.initials: R
authors.lastname: Guchenko
keywords: Design of experiment, Bayesian optimal design; gradient methods; model discrimination; model uncertainty