Design of Experiments and Canonical Moments

DMS 9626784 Studden本研究由两个相关部分组成：一部分涉及实验设计，另一部分涉及统计与概率中的正则矩。 在设计领域的研究涉及复杂的计算机代码的分析，在回归理论和刚性设计的分析合理的功能的使用。 复杂的计算机代码进行分析，以最佳地选择输入值用于进一步的预测目的。 该理论涉及到随机过程、多维插值理论和逼近理论的应用。第二部分涉及使用规范化的矩分布的真实的线称为典范矩。这些已成功地用于设计实验中的一维多项式回归。 本研究探讨矩理论和随机游动中一些未回答的问题。 实验设计问题一般涉及如何选择进行哪些实验以获得最大的信息在最小的cost.The本研究涉及复杂的计算机代码的分析，其中的问题是决定最佳的输入值，以预测在其他可能的输入值的结果。 这与高性能计算密切相关，这是NSF当前的战略领域之一。

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.