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

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