Bayesian D-optimal designs for exponential regression models.

*(English)*Zbl 0900.62408Summary: 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.

##### MSC:

62K05 | Optimal statistical designs |

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\textit{H. Dette} and \textit{H. M. Neugebauer}, J. Stat. Plann. Inference 60, No. 2, 331--349 (1997; Zbl 0900.62408)

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