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Bayesian D-optimal designs for exponential regression models

✍ Scribed by Holger Dette; H.-M. Neugebauer

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
875 KB
Volume
60
Category
Article
ISSN
0378-3758

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✦ Synopsis

We consider the Bayesian D-optimal design problem for exponential growth models with one. two or three parameters. For the one-parameter model conditions on the shape of the density of the prior distribution and on the range of its support are given guaranteeing that a one-point design is also Bayesian D-optimal within the class of all designs. In the case of two parameters the best two-point designs are determined and for special prior distributions it is proved that these designs are Bayesian D-optimal. Finally, the exponential growth model with three parameters is investigated. The best three-point designs are characterized by a nonlinear equation. The global optimality of these designs cannot be proved analytically and it is demonstrated that these designs are also Bayesian D-optimal within the class of all designs if gamma-distributions are used as prior distributions.

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