The goal of this research is to provide the theory and the methods for finding efficient experimental designs for non-linear problems. In the non-linear case, the efficiency of a design depends on the values of the unknown parameters and a traditional approach to the problem has been to design for a best guess of the parameters. A Bayesian approach uses a prior distribution and takes into account not only the best guess but also the uncertainty associated with the best guess. Bayesian designs can also be interpreted in a non-Bayesian framework as designs that minimize the average asymptotic variances. The authors will extend their results on the important special problem of designing an experiment where the response increases with dose according to a logistic distribution. The primary tools they must further develop in order to obtain successful extensions are optimization algorithms. They first intend to work on sequential designs. This research will permit more information to be incorporated into the design of efficient experiments. Inproved computational capabilities over the last decade makes this work possible. Prior to the computer revolution, scientific experiments were simply designed with computational feasibility a major consideration. Not only has this limitation been largely eliminated, but also larger and more complex experiments are being conducted. Efficient designs for modern science are critical for sound utilization of the nation's research and development funds.
