Bayesian D-Optimal Designs for Poisson Regression Models

Abstract

By incorporating informative and/or historical knowledge of the unknown parameters, Bayesian experimental design under the decision-theory framework can combine all the information available to the experimenter so that a better design may be achieved. Bayesian optimal designs for generalized linear regression models, especially for the Poisson regression model, is of interest in this article. In addition, lack of an efficient computational method in dealing with the Bayesian design leads to development of a hybrid computational method that consists of the combination of a rough global optima search and a more precise local optima search. This approach can efficiently search for the optimal design for multi-variable generalized linear models. Furthermore, the equivalence theorem is used to verify whether the design is optimal or not.

Keywords:

• Bayesian optimal design
• D-optimal design
• Design efficiency
• Generalized linear model
• Genetic algorithm
• Poisson regression model

Acknowledgment

We would like to thank the Associate Editor and the referee for their helpful comments and suggestions. Their repeated efforts to make this manuscript better are really appreciated. We would also like to thank J. P. Morgan and Tao Lin, both at Virginia Tech, for useful discussions.

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.