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April 2007 On the number of support points of maximin and Bayesian optimal designs
Dietrich Braess, Holger Dette
Ann. Statist. 35(2): 772-792 (April 2007). DOI: 10.1214/009053606000001307

Abstract

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 for these parameters is available. On interval parameter spaces, 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 in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper, we present analytic tools which are used to prove this phenomenon in concrete situations. The proposed methodology can be used to explain many empirically observed results in the literature. Moreover, it explains why maximin D-optimal designs are usually supported at more points than Bayesian D-optimal designs.

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Dietrich Braess. Holger Dette. "On the number of support points of maximin and Bayesian optimal designs." Ann. Statist. 35 (2) 772 - 792, April 2007. https://doi.org/10.1214/009053606000001307

Information

Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62074
MathSciNet: MR2336868
Digital Object Identifier: 10.1214/009053606000001307

Subjects:
Primary: 62K05

Keywords: Bayesian optimal design , maximin optimal design , nonlinear models

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 2 • April 2007
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