Collaborative research: A major leap forward: Optimal designs for correlated data, multiple objectives, and multiple covariates

设计性实验是许多研究领域科学过程中不可或缺的一部分，如生物科学、健康科学、社会科学、工程学、市场营销、教育等。精心挑选的设计有助于收集数据，以固定成本最大限度地增加感兴趣的科学问题的信息，或最大限度地减少所需信息水平的成本。许多实验处理相关数据，多个目标，或多个协变量，但鲜为人知的是，在这样的设置良好的设计识别。这个项目建立了如何为最常用的统计模型找到这些类型问题的有效设计。在这个项目中开发的工具有一个巨大的潜力，对社会的影响，因为设计的实验经常被用来进一步了解在许多不同的领域。该项目的结果将通过易于使用的软件提供给其他领域的研究人员，该软件实现了开发的算法。研究生将被培养成为实验设计的研究人员。该项目的成果构成了对实验优化设计的理解和知识的重大飞跃。主要研究者和其他人最近的贡献对非线性和广义线性模型实验的最优设计的进步产生了重大影响。然而，这些结果在很大程度上仅限于（i）独立数据;（ii）使用单一最优性标准;（iii）使用单一协变量。虽然这些结果本身就很重要，但该项目将扩展方法和工具，以解决相关数据，多目标和多协变量的问题。后者可以由实验者可以选择的协变量和在设计阶段已知或未知的协变量的混合组成，不能由实验者控制。初步结果表明，这是采取这些具有挑战性但至关重要的步骤的适当时机。为这些类型的问题建立一个衍生和确定最佳设计的框架将为我们的集体设计工具箱提供一个急需的补充。目前的结果是非常稀疏，只有非常专业的问题，主要是由数学的可行性。该项目开发工具，以选择有效的设计模型和条件，是远远超过那些已经考虑到目前为止。

Designed experiments form an integral part of the scientific process in many areas of research, such as the biological sciences, the health sciences, the social sciences, engineering, marketing, education, and others. A well-chosen design facilitates the collection of data that maximizes the information for the scientific questions of interest at a fixed cost, or that minimizes the cost for a desired level of information. Many experiments deal with correlated data, multiple objectives, or multiple covariates, but little is known about the identification of good designs in such settings. This project establishes how to find efficient designs for these types of problems for the most commonly used statistical models. The tools developed in this project have a tremendous potential for impact on society because designed experiments are used so often to further knowledge in many different fields. Results from the project will be made available to researchers in other areas through easy-to-use software that implements algorithms that are developed. Graduate students will be trained to become researchers in design of experiments. The outcomes of this project constitute a major leap forward in understanding and knowledge of optimal design of experiments. Recent contributions by the principal investigators and others have had a significant impact on the advancement of optimal design of experiments for nonlinear and generalized linear models. However, these results have for the most part been limited to (i) independent data; (ii) use of a single optimality criterion; and (iii) use of a single covariate. While these results are arguably important in their own right, this project will extend methods and tools to problems with correlated data, multiple objectives, and multiple covariates. The latter could consist of a mix of covariates that can be chosen by the experimenter and covariates that, known or unknown at the design stage, cannot be controlled by the experimenter. Preliminary results indicate that this is an opportune time to make these challenging but critical steps. Building a framework for deriving and identifying optimal designs for these types of problems will provide a much needed addition to our collective design toolbox. Current results are very sparse and only for very specialized problems that are mostly motivated by mathematical feasibility. The project develops tools to select efficient designs for models and conditions that are far more realistic than those that have been considered so far.