Bayesian Designs for Approximate Normality

Abstract

In many experimental design problems, the primary interest is in estimating functions of the parameters and a design is selected according to some optimality criterion. The assumption that parameter estimates are approximately normally distributed is often used to find optimal designs, as well as simplify data analysis. How well this approximation holds for small to moderate sample sizes depends on the intrinsic and parameter-effects curvatures. These measures depend on both the parameterization used as well as the experimental design. For a particular parameterization of interest, these curvatures can be reduced by the choice of the experimental design. A Bayesian approach is taken to find designs that optimize the primary design criterion subject to satisfying constraints based on these curvature measures, with the goal of improving normal approximations. The constrained designs depend on the sample size, but as the sample size increases the constraints are satisfied. A nonlinear regression example is used to illustrate the approach.