Factorial Designs, An Indicator Function Approach

因子设计，一种指标函数方法

• 批准号: 0306306
• 负责人: Kenny Ye
• 金额: $ 13.72万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0306306&HistoricalAwards=false
• 关键词: Factorial; Designs; Indicator; Function; Approach

Proposal ID: DMS-0306306PI: Kenny YeTitle: Factorial Designs, An Indicator Function ApproachAbstract:Recent researches show that indicator functions are very effective tools for studying theoretical properties of factorial designs. Initially proposed by Fontana, Pistone and Rogantin (2000) and later modified and generalized by the investigator and his collaborators, indicator functions provide a unified representation for all factorial designs, regular or non-regular, two-level, multi-level or mixed-level. The aliasing structure of a factorial design could be clearly revealed by expanding its indicator function with respect to an orthogonal polynomial basis. An important application of this approach is to study geometric structures of orthogonal arrays, which are essential for response surface methodology but have been largely overlooked in the past. The proposed research seeks not only in depth understanding of factorial designs but also discovery of many new efficient designs. The project pursues three main tasks. First, continue development of theoretical foundation of the indicator function approach and apply it to different types of designs including blocked designs and split-plot designs. Second, generalize minimum aberration criteria to all factorial designs. The criteria should be based on the intrinsic structure of a design but not on a priori specified models. Links to design efficiency and estimation capacity will be thoroughly studied, both theoretically and empirically. Third, develop and apply a sequential algorithm to construct a complete catalogue of non-isomorphic orthogonal arrays of small run sizes.Factorial designs are vital for investigations in both life and physical sciences, as well as in agricultural and industrial studies. Non-regular designs have an advantage over regular designs at the screening and exploration stage of an investigation. Besides many traditional areas that factorial designs are applied, one particular area that will benefit is biomedical research, in which exploration and screening investigations are pervasive, especially with new technologies such as microarrays. Many new, more efficient designs are to be generated in the proposed research and be disseminated through interdisciplinary collaboration with other members of the scientific communities and interactions with industries. An integrated part of the proposed research is to adopt the indicator function approach in the curriculum of standard experimental design courses. Such change from current curriculum will promote the future applications of non-regular designs in practice. The investigator is also committed to involve students in the proposed research, especially those from underrepresented groups. In addition, the proposed research is expected to open interdisciplinary communication between algebraic geometricians and statisticians.

提案ID：DMS-0306306 PI： Kenny YeTitle：析因设计，一种指示函数方法摘要：近年来的研究表明，指示函数是研究析因设计理论性质的有效工具。指标函数最初由丰塔纳、Pistone和Rogantin（2000）提出，后来由研究者及其合作者进行了修改和推广，它为所有的析因设计提供了一个统一的表示，无论是正规的还是非正规的，两水平的，多水平的还是混合水平的。通过将析因设计的指示函数在正交多项式基上展开，可以清楚地揭示析因设计的混叠结构。这种方法的一个重要应用是研究正交表的几何结构，这是响应面方法学必不可少的，但在过去很大程度上被忽视。该研究不仅寻求对析因设计的深入理解，而且还发现了许多新的有效设计。该项目追求三项主要任务。首先，继续发展指示函数法的理论基础，并将其应用于不同类型的设计，包括区组设计和裂区设计。其次，将最小像差准则推广到所有析因设计。这些标准应基于设计的内在结构，而不是基于先验的特定模型。将从理论和经验两方面对设计效率和估算能力的联系进行深入研究。第三，开发和应用一个顺序算法来构造一个完整的小试验规模的非同构正交表目录。析因设计对于生命科学和物理科学的研究以及农业和工业研究都是至关重要的。在调查的筛选和勘探阶段，非常规设计优于常规设计。除了应用析因设计的许多传统领域外，一个特别受益的领域是生物医学研究，其中探索和筛选调查非常普遍，特别是在微阵列等新技术方面。在拟议的研究中将产生许多新的、更有效的设计，并通过与科学界其他成员的跨学科合作和与工业界的互动加以传播。建议研究的一个组成部分是在标准实验设计课程中采用指标函数法。这种对现有课程的改变将促进非常规设计在实践中的应用。研究人员还致力于让学生参与拟议的研究，特别是那些代表性不足的群体。此外，拟议中的研究有望打开代数几何学家和统计学家之间的跨学科交流。