Design of Mixture Experiments Using Bayesian<i>D</i>-Optimality

Abstract

A Bayesian modification is used to reduce the dependency of D-optimal designs on the assumed model. We study the performance of these Bayesian D-optimal designs with respect to the total squared error of prediction and the distribution of information throughout the factor space. The study investigates three and four component, constrained and unconstrained mixture experiments. Some of the designs evaluated perform extremely well with respect to these characteristics. Compared to standard D-optimal designs they produce significantly smaller bias errors, allow the fitting of a larger number of higher order terms, improve the coverage of the factor space, and still have very good variance properties. Practical recommendations are provided for the practitioner.