Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are unsuitable here because they often focus on one type of response. In this paper, we develop a Bayesian D-optimal design method for experiments with one continuous and one binary response. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterion has meaningful interpretations regarding the D-optimality for the models for both types of responses. An efficient point-exchange search algorithm is developed to construct the local D-optimal designs for given parameter values. Global D-optimal designs are obtained by accumulating the frequencies of the design points in local D-optimal designs, where the parameters are sampled from the prior distributions. The performances of the proposed methods are evaluated through two examples.
翻译:系统有定量和定性响应在许多应用中被广泛遇见。当进行实验研究这种系统时需要设计实验方法。经典的实验设计方法在这里不适用,因为它们通常只关注一种响应类型。在本文中,我们开发了一种贝叶斯D-optimal实验设计方法,该方法适用于具有一个连续和一个二元响应的实验。我们考虑了未知参数的无信息和共轭信息先验分布。所提出的设计标准在两种响应类型的模型的D-最优性方面具有有意义的解释。开发了一种有效的点交换搜索算法,用于构建给定参数值的局部D-optimal设计。通过从先验分布中对参数进行采样,我们获得全局D-optimal设计,其中积累了局部D-optimal设计中设计点的频率。我们通过两个示例评估了所提出方法的性能。