Bayesian D-Optimal Designs for Poisson Regression Models

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.