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：在众多应用中，同时具有定量和定性响应的系统广泛存在。当开展实验研究此类系统时，需要实验设计方法。经典实验设计方法通常只关注一种类型的响应，因此不适用于此。本文针对一个连续响应和一个二元响应的实验，提出了一种贝叶斯D最优设计方法。我们同时考虑了未知参数的无信息共轭先验分布和有信息共轭先验分布。所提出的设计准则对于这两种响应类型的模型，从D最优性角度具有明确的解释意义。我们开发了一种高效的点交换搜索算法，用于构造给定参数值下的局部D最优设计。通过从先验分布中采样参数，并累积局部D最优设计中设计点的频率，可获得全局D最优设计。通过两个实例评估了所提出方法的性能。