Design of Experiments and Canonical Moments

实验和典型矩的设计

• 批准号: 9626784
• 负责人: William Studden
• 金额: $ 6.6万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626784&HistoricalAwards=false
• 关键词: Design; Experiments; Canonical; Moments

DMS 9626784 Studden This research is composed of two related parts: one part deals with the design of experiments and the other deals with canonical moments in Statistics and Probability. The research in the design area involves the analysis of complex computer codes, the use of rational functions in regression theory and the analysis of rigid designs. Complex computer codes are analysed asympotically in order to optimally choose input values to use for further prediction purposes. The theory involves the use of stochastic processes, multidimensional interpolation theory and approximation theory. The second part involves the use of normalized moments of distributions on the real line called canonical moments. These have been used successfully in designing experiments in one dimensional polynomial regression. The present study investigates some unanswered questions in moment theory and random walks. Experimental design problems in general involve how to choose which experiments to conduct to obtain maximal information at minimal cost.The present research involves the analysis of complex computer codes where the problem is to decide on optimal input values to predict the outcome at other possible input values. This relates significantly to high performance computing which is one of NSF's current strategic areas.

DMS 9626784 Studden这项研究由两个相关部分组成：一个部分涉及实验的设计，而其他涉及统计和概率的规范时刻。 设计领域的研究涉及对复杂计算机代码的分析，在回归理论中使用合理功能以及对刚性设计的分析。 对复杂的计算机代码进行不可分割的分析，以便最佳选择用于进一步预测目的的输入值。 该理论涉及随机过程的使用，多维插值理论和近似理论。第二部分涉及在称为规范矩的真实线上使用归一化的分布矩。这些已成功用于设计一维多项式回归的实验。 本研究调查了时刻理论和随机步行中的一些未解决的问题。 通常，实验设计问题涉及如何以最低成本选择进行最大信息进行哪些实验。当前的研究涉及对复杂计算机代码的分析，该问题是在其中确定最佳输入值以预测其他可能输入值的结果。 这与NSF当前战略领域之一的高性能计算非常重要。