Abstract
Bayesian optimal designs for nonlinear regression models are of some interest and importance in the statistical literature. Numerical methods for their construction are well-established, but very few analytical studies have been reported. In this paper, we consider an exponential growth model used extensively in the modelling of simple organisms, and examine the explicit form of the Bayesian D-optimal designs. In particular, we show that D θ-optimal designs for this model are balanced two-point designs for all values of the parameters. We further derive explicit expressions for Bayesian D-optimal designs which are based on exactly two points of support, and provide necessary and sufficient conditions for such designs to exist. We illustrate our results by means of two examples.
Published Version
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