Simulation-Based Optimal Design Using a Response Variance Criterion

Abstract

Classical optimal design criteria suffer from two major flaws when applied to nonlinear problems. First, they are based on linearizing the model around a point estimate of the unknown parameter and therefore depend on the uncertain value of that parameter. Second, classical design methods are unavailable in ill-posed estimation situations, where previous data lack the information needed to properly construct the design criteria. Bayesian optimal design can, in principle, solve these problems. However, Bayesian design methods are not widely applied, mainly due to the fact that standard implementations for efficient and robust routine use are not available. In this article, we point out a concrete recipe for implementing Bayesian optimal design, based on the concept of simulation-based design introduced by Muller, Sanso, and De Iorio (2004). We develop further a predictive variance criterion and introduce an importance weighting mechanism for efficient computation of the variances. The simulation-based approach allows one to start the model-based optimization of experiments at an early stage of the parameter estimation process, in situations where the classical design criteria are not available. We demonstrate that the approach can significantly reduce the number of experiments needed to obtain a desired level of accuracy in the parameter estimates. A computer code package that implements the approach in a simple case is provided as supplemental material (available online).