Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a D -optimal design for a dose-response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian D -optimality. While we focus on D -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will be lost.

中文翻译：

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设计热图：最优设计问题的简单可视化

最佳实验设计通常是正式且具体的，对于实际实验者来说直观上并不合理。然而，即使在理论上，与严格最优设计的设计点相比，通常也存在许多不同的可能设计点提供相同或几乎相同的信息。在实际应用中，这可以用来找到数学最优性和实际要求（包括实验者的偏好）之间折衷的设计。为此，我们提出了一种基于导数的设计空间二维图形表示，在已知任何最佳设计的情况下，该表示将显示设计空间的哪些区域与良好的设计相关以及这些区域如何相互关联。虽然现有的等价定理已经允许仅就设计点的相关性进行这样的说明，但我们的方法还显示不同的设计点是否贡献相同类型的信息，从而允许针对实际应用调整设计，特别是在分裂方面以及设计要点的结合。我们在毒理学试验中展示了该方法，其中要求对由四参数对数逻辑函数建模的剂量反应实验进行 D 最优设计。由于这些设计需要预先估计相关参数，而这在实际情况下很难获得，因此我们还讨论了我们的表示法对贝叶斯 D 最优性标准的适应。虽然我们关注 D 最优性，但该方法原则上也适用于不同的最优性标准。然而，许多计算和图形的简单性将会丢失。