Computation of Optimum in Average Designs for Experiments with Finite Design Space

Abstract

For Generalized Linear Models (GLM) optimum designs generally depend on the true but unknown parameter values. If a prior distribution for the parameters is available, it is possible to use a design that is optimum in average. If, in particular, the prior is uniform, the corresponding optimum design is termed a Laplace design. The purpose of this article is to indicate a Newton-Raphson procedure for computation of optimum in average designs for inference about parameters in a GLM when the design space is finite and to study the efficiency properties of Laplace designs in comparison with designs that use a uniform allocation of observations. Three numerical examples are presented, viz. two control group experiments and a Latin square experiment. The efficiency comparisons in these examples indicate that the Laplace designs are likely to be more efficient, when the prior information about the parameters is correct.

Keywords:

• Generalized Linear Models
• D_A -optimum
• Newton-Raphson