  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.
