Bayesian two-stage optimal design for mixture models

Abstract

In this paper, a Bayesian two-stage D–D optimal design for mixture experimental models under model uncertainty is developed. A Bayesian D-optimality criterion is used in the first stage to minimize the determinant of the posterior variances of the parameters. The second stage design is then generated according to an optimalityprocedure that collaborates with the improved model from the first stage data. The results show that a Bayesian two-stage D–D-optimal design for mixture experiments under model uncertainty is more efficient than both the Bayesian one-stage D-optimal design and the non-Bayesian one-stage D-optimal design in most situations. Furthermore, simulations are used to obtain a reasonable ratio of the sample sizes between the two stages.

Keywords:

• Bayesian optimal design
• mixture experiments
• two-stage design