Design construction and model selection for small mixture-process variable experiments with high-dimensional model terms

TL;DR: In this article , the design construction and model selection for mixture-process variable experiments where the number of variables is large is considered and the generalized Bayesian-D criterion is employed to choose the optimal design and apply the Bayesian analysis method to select the best model.

Abstract: Abstract This paper considers the design construction and model selection for mixture-process variable experiments where the number of variables is large. For such experiments the generalized least squares estimates cannot be obtained and hence it will be difficult to identify the important model terms. To overcome these problems, here we employ the generalized Bayesian-D criterion to choose the optimal design and apply the Bayesian analysis method to select the best model. Two algorithms are developed to implement the proposed methods. A fish-patty experiment demonstrates how the Bayesian approach can be applied to a real experiment. Simulation studies show that the proposed method has a high power to identify important terms and well controls the type I error.