Design Methodology for Computer and Physical Experiments

计算机和物理实验的设计方法

• 批准号: RGPIN-2015-03903
• 负责人: Tang, Boxin
• 金额: $ 1.82万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=666493
• 关键词: Design; Methodology; Computer; Physical; Experiments

Statistical models provide powerful tools that enable researchers to investigate complex systems from almost every imaginable field of studies in natural sciences, engineering, social sciences and humanities. A crucial step in the process of model building is the data collection. No matter how elaborate and sophisticated a model building process is, a statistical model contains no more information than what the data can offer. Experimental design is an area of statistics devoted to the study of efficient methods for informative data collection and corresponding methods of data analysis. ****Fractional factorial designs are a class of experimental plans for exploring the relationship between a response variable and a set of explanatory variables. Their practical usefulness and theoretical importance are well documented in the literature. The first broad objective of this research proposal is to extend the existing methods and develop new methodology for fractional factorial designs. Two focal points of the proposed research are optimality and robustness. In particular, we will investigate optimality and robustness of fractional factorial designs under a recently developed baseline parametrization. ***Computer models are increasingly popular nowadays. When the computer code representing a computer model is expensive to run, it is desirable to build a cheaper surrogate model. Computer experiments are concerned with the building of a statistical surrogate model based on the data consisting of a set of carefully selected inputs and the corresponding outputs from running a computer code. Space-filling designs have been widely accepted as appropriate designs for computer experiments. The second broad objective of the proposed research is to consolidate the existing methods and develop new methods for constructing space-filling designs. Particular attention will be paid to two classes of space-filling designs, namely, strong orthogonal arrays and mappable nearly orthogonal arrays.***Training HQP and disseminating research results are two important aspects of the proposed research, which will be accomplished by involving students in research activities and by collaborating with statistical practitioners. Completion of the proposed research will shed new light on design theory, result in new designs for computer and physical experiments, and promote further applications of design methodology.*** *** **

统计模型提供了强大的工具，使研究人员能够从自然科学，工程学，社会科学和人文科学的几乎每个可以想象的研究领域研究复杂的系统。模型构建过程中的一个关键步骤是数据收集。无论模型构建过程多么复杂，统计模型所包含的信息都不会超过数据所能提供的信息。实验设计是统计学的一个领域，致力于研究有效的信息数据收集方法和相应的数据分析方法。* 部分因子设计是一类用于探索响应变量和一组解释变量之间关系的实验计划。它们的实际用途和理论重要性在文献中有很好的记载。本研究建议的第一个广泛目标是扩展现有方法并开发新的部分析因设计方法。研究的两个重点是最优性和鲁棒性。 特别是，我们将调查的最优性和稳健性的部分析因设计下最近开发的基线参数化。**当表示计算机模型的计算机代码运行起来很昂贵时，希望构建更便宜的代理模型。计算机实验涉及基于由一组精心选择的输入和运行计算机代码的相应输出组成的数据的统计代理模型的构建。空间填充设计已被广泛接受为计算机实验的适当设计。拟议的研究的第二个广泛的目标是巩固现有的方法，并开发新的方法来构建空间填充设计。将特别注意两类空间填充设计，即强正交表和可映射近正交表。培训HQP和传播研究成果是拟议研究的两个重要方面，这将通过让学生参与研究活动和与统计从业人员合作来完成。该研究的完成将为设计理论提供新的思路，为计算机和物理实验提供新的设计，并促进设计方法学的进一步应用。*** **