## The Annals of Statistics

### On the number of support points of maximin and Bayesian optimal designs

#### 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.

#### Article information

Source
Ann. Statist. Volume 35, Number 2 (2007), 772-792.

Dates
First available in Project Euclid: 5 July 2007

http://projecteuclid.org/euclid.aos/1183667293

Digital Object Identifier
doi:10.1214/009053606000001307

Mathematical Reviews number (MathSciNet)
MR2336868

Zentralblatt MATH identifier
1117.62074

Subjects
Primary: 62K05: Optimal designs

#### Citation

Braess, Dietrich; Dette, Holger. On the number of support points of maximin and Bayesian optimal designs. Ann. Statist. 35 (2007), no. 2, 772--792. doi:10.1214/009053606000001307. http://projecteuclid.org/euclid.aos/1183667293.

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