On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models - Dietrich Braess; Holger Dette (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2004)
We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information (i.e. a larger range for the parameter space in the maximin criterion or a larger variance of the prior distribution in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper we present a rigorous proof of this phenomenon and show that in many nonlinear regression models the number of support points of Bayesian- and maximin D-optimal designs can become arbitrarily large if less prior information is available. Our results also explain why maximin D-optimal designs are usually supported at more different points than Bayesian D-optimal designs.
Keywords: 519; Bayesian optimal design; maximin optimal design; nonlinear regression; Regression; Nichtlineares Verfahren; Theorie