Bayesian sequential [formula omitted]- [formula omitted] optimal model-robust designs

Abstract

Alphabetic optimal design theory assumes that the model for which the optimal design is derived is known. However in practice, this assumption may not be credible, as models are rarely known in advance. Therefore, optimal designs derived under the classical approach may be the best design but for the wrong assumed model. The Bayesian two-stage approach to design experiments for the general linear model when initial knowledge of the model is poor, is reviewed and extended. A Bayesian optimality procedure that works well under model uncertainty is used in the first stage and the second stage design is then generated from an optimality procedure that incorporates the improved model knowledge from the first stage. In this way, the Bayesian D - D optimal model-robust design is developed. Results show that the Bayesian D - D optimal designs are in general superior in performance to the classical one-stage D -optimal and the one-stage Bayesian D -optimal designs. The ratio of sample sizes for the two stages and the minimum sample size desirable in the first stage is also examined in a simulation study.