Mathematical Sciences: Studies in Efficient and Optimal Design and Analysis of Experiments

仔细设计实验可以在实验完成时产生更直接、更有效和更精确的分析；本文在几个重要的实验情况下给出了优化设计的数学结构。每当在每个实验单元上进行一系列观察或每当计划对曲线进行集体分析时，都可以使用最佳重复测量设计。在许多情况下，最大的不确定性来源在于模型的初始选择，设计将被构建为对假设模型的偏差具有鲁棒性。在某些情况下，一些非常理想的观察是不可能的或过于昂贵的，标准和算法将开发使用组合和优化理论，以选择“近最优”设计。

Careful design of an experiment may yield a more direct as well as a more efficient and precise analysis at the experiment's completion; this research gives mathematical constructions for optimal designs in several important experimental situations. Optimal repeated measurements designs can be used whenever sequences of observations are made on each experimental unit or whenever a collective analysis of curves is planned. For the many circumstances where the greatest source of uncertainty lies in the initial choice of model, designs will be constructed which are robust against deviations from a postulated model. For situations in which some highly desirable observations are impossible or excessively costly, criteria and algorithms will be developed using combinatorial and optimization theories for choice among "near-optimal" designs.