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

协作研究：重大飞跃：相关数据、多目标和多协变量的优化设计

基本信息

批准号：
1407518
负责人：
Min Yang
金额：
$ 21.1万
依托单位：
University of Illinois at Chicago
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2014
资助国家：
美国
起止时间：
2014-07-15 至 2018-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407518&HistoricalAwards=false
关键词：
Collaborative research major leap forward

项目摘要

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.

在许多研究领域，例如生物科学，健康科学，社会科学，工程，营销，教育等许多研究领域，设计实验构成了科学过程的组成部分。精心挑选的设计有助于收集数据，以固定成本最大程度地提高了感兴趣的科学问题信息，或者最大程度地减少了所需信息水平的成本。许多实验涉及相关的数据，多个目标或多个协变量，但是对于在这种情况下识别良好设计的识别知之甚少。该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。该项目中开发的工具对社会产生了巨大的影响，因为设计实验经常用于在许多不同领域的知识。该项目的结果将通过实现开发算法的易于使用的软件提供给其他领域的研究人员。研究生将接受培训，成为实验设计的研究人员。该项目的结果构成了对实验最佳设计的理解和知识的重大飞跃。首席研究人员和其他人的最新贡献对非线性和广义线性模型的实验最佳设计的进步产生了重大影响。但是，这些结果在很大程度上仅限于（i）独立数据。（ii）使用单个最优标准；（iii）使用单个协变量。尽管这些结果本身就是重要的，但该项目将将方法和工具扩展到相关数据，多个目标和多个协变量的问题。后者可以由实验者可以选择的协变量组成，并使协变量在设计阶段已知或未知的协变量无法由实验者控制。初步结果表明，这是做出这些具有挑战性但至关重要的步骤的合适时机。建立一个用于得出和确定这些类型问题的最佳设计的框架将为我们的集体设计工具箱提供急需的补充。当前的结果非常稀疏，仅出于非常专业的问题，这些问题主要是由数学可行性激发的。该项目开发了为模型和条件选择高效设计的工具，这些设计比迄今为止被认为的工具更现实。