Design and Analysis of Complex Experiments: Branching Factors and Functional Responses

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。实验的统计设计与分析是科学发现中常用的有效工具。技术和计算能力的快速发展使得许多复杂的实验成为可能，例如那些具有分支因子和功能反应的实验。它还提出了许多新的挑战。该提案的主要目标是开发一套新颖有效的统计方法，以应对新出现的挑战，从而加速许多使用实验研究的学科的发现。研究计划由两部分组成。研究的第一部分集中在分支和嵌套因素的实验设计和分析。在许多复杂的实验中，某些因子只存在于另一个因子的水平之内。这些因子通常称为嵌套因子。嵌套其他因子的因子称为分支因子。分支和嵌套因子的实验设计和分析在许多复杂系统中是至关重要的，并且在文献中没有得到太多关注。在本提案的第一部分中，提出了新的设计、理论、组合和算法构造策略以及结构化建模类别，可以考虑复杂实验中的分支和嵌套结构并有效识别重要因素。研究的第二部分着重于功能反应的计算机实验分析。物理实验可能是昂贵和耗时的;因此，计算机实验已被广泛用作经济的替代品。许多计算机实验响应都是以函数形式收集的。然而，由于现有的大多数建模技术都集中在单一输出上，因此关于用功能反应建模计算机实验的文献仍然很少。虽然有一些降维技术的功能性反应，他们不占一个重要的功能，确定性的输出，计算机实验。为了解决这个问题，提出了一种顺序技术，它提供了一个插值模型。它还采用了一种新的迭代过程，从而享有很高的计算效率。新的设计类，设计理论，组合和算法的建设方法，并在这项研究中提出的结构化模型似乎是第一次系统的调查与分支和嵌套的因素实验。它们可以为研究问题开辟新的途径，为理论和应用研究注入活力。提出的计算机功能反应实验序贯建模方法考虑了计算机实验的特点，具有较高的计算效率。这是一个创新的概念，可以导致新的研究功能数据分析。这两种方法都适用于各种科学领域，如电子封装，生物力学工程设计，野火控制和流感建模。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Statistical design and analysis of experiments is an effective and commonly used tool in scientific discoveries. The rapid growth in technology and computing power has made available many complex experiments, such as those with branching factors and functional responses. It also poses many new challenges. The primary objective of this proposal is to develop a set of novel and efficient statistical methods to tackle the emerging challenges and thus accelerate discoveries in many disciplines that use experimental investigation. The research plan consists of two parts. The first part of the research focuses on design and analysis of experiments with branching and nested factors. In many complex experiments, some of the factors exist only within the level of another factor. Such factors are often called nested factors. A factor within which other factors are nested is called a branching factor. Design and analysis of experiments with branching and nested factors are crucial in many complex systems and have not received much attention in the literature. In the first part of this proposal, new classes of designs, theory, combinatorial and algorithmic construction strategies, and structured modeling are proposed that can take into account the branching and nested structure in a complex experiment and identify important factors effectively. The second part of the research focuses on the analysis of computer experiments with functional responses. Physical experiments can be expensive and time-consuming; thus, computer experiments have been widely used as economical alternatives. Many computer experiment responses are collected in a functional form. However, literature on modeling computer experiments with functional responses remains scarce as most of the existing modeling techniques focus on single outputs. Although there are some dimension reduction techniques for functional responses, they do not account for an important feature, the deterministic outputs, of computer experiments. To address this issue, a sequential technique is proposed, which provides an interpolating model. It also incorporates a novel iterative procedure and thus enjoys great computational efficiency.The new class of designs, design theory, combinatorial and algorithmic construction methods, and structured models proposed in this research appears to be the first systematic investigation of experiments with branching and nested factors. They can open new avenues for studying problems that energize both theoretical and applied research. The proposed sequential modeling technique for computer experiments with functional responses takes into account the special features in computer experiments and enjoys great computational efficiency. It is an innovative concept which can lead to new research in functional data analysis. Both methods are readily applicable to a variety of scientific fields, such as electronic packaging, biomechanical engineering design, wildfire control, and influenza modeling.