Most research in design of experiments focuses on appropriate designs for a system with just one type of response, rather than multiple responses. In a decision-making process, relying on only one objective can lead to oversimplified, suboptimal choices that ignore important considerations. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest often does not have a single definitive answer, particularly when the response variables have different distributions. Each of these response distributions imposes different requirements on the experimental design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal and binomial distributions are considered as potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the logistic regression model, a weighted criterion is implemented in a coordinate-exchange algorithm. Designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied for the Bayesian D-criterion is also explored.

中文翻译：

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正态和二项式情况下双响应系统的优化设计

大多数实验设计研究都侧重于对只有一种类型的响应而不是多种响应的系统进行适当的设计。在决策过程中，仅依赖一个目标可能会导致过于简单化、次优的选择，而忽略了重要的考虑因素。因此，当对多种类型的响应感兴趣时，为实验构建设计的问题通常没有一个明确的答案，特别是当响应变量具有不同的分布时。这些响应分布中的每一个都对实验设计提出了不同的要求。计算机生成的优化设计是经典设计不理想的不太标准的场景的流行设计选择。这项工作为双响应系统的实验设计提供了一种新方法。正态分布和二项分布被视为潜在响应。使用线性模型的 D 准则和逻辑回归模型的贝叶斯 D 准则，在坐标交换算法中实现加权准则。对不同权重的设计进行评估和比较。还探讨了设计对提供给贝叶斯 D 标准的先验的敏感性。