Bayesian D-Optimal Designs for Generalized Linear Models with a Varying Dispersion Parameter

In this article we extend the results of (1995) concerning D-optimum designs for heteroscedastic regression models. They introduced a variety of D-optimality criteria, under the hypothesis of Gaussian errors, when the mean response and the variance are parametric functions of possibly different sets of explanatory variables. The aim of this paper is to extend such ideas under other distributional assumptions rather than Gaussian. We regard an unknown likelihood but suppose the relationship between the mean response and the variance is known. Bayesian D-optimum designs for models pertaining to the exponential family are then proposed. This methodology is only feasible by applying the concept of extended quasi-likelihood, first proposed in (1987). A potential area of application of the results proposed here lies in experimental design in off-line quality control.