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In nonlinear regression models the Fisher information depends on theparameters of the model. Consequently, optimal designs maximizing somefunctional of the information matrix cannot be implemented directly but requiresome preliminary knowledge about the unknown parameters. Bayesian optimalitycriteria provide an attractive solution to this problem. These criteria dependsensitively on a reasonable specification of a prior distribution for the modelparameters which might not be available in all applications. In this paper weinvestigate Bayesian optimality criteria with non-informative prior dis-tributions. In particular, we study the Jeffreys and the Berger-Bernardo priorfor which the corresponding optimality criteria are not necessarily concave.Several examples are investigated where optimal designs with respect to the newcriteria are calculated and compared to Bayesian optimal designs based on auniform and a functional uniform prior.

Optimal designs for nonlinear regression models with respect to non-informative priors