Optimal Weighted Bayesian Design Applied to Dose-response-curve Analysis

Designs for nonlinear regression models depend on some prior information about the unknown parameters. There are three primary methods for accounting for this: The locally optimal designs, globally optimal Bayesian designs, and sequential procedures. If prior knowledge about the parameters is available from former experiments, Bayesian designs integrate this information most eeciently. If the experiments have been performed with replicate measurements, these results can be used to take a heteroscedastic error model into account. We propose a globally optimal, weighted Bayesian design for a heteroscedastic error structure, which can be extended to sequential design procedures. These concepts have been motivated by an application problem in pharmacology: Given a limited number of treatments in bioassay-experiments, an optimal design for dose-response-curves should be determined.