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

仔细的实验设计可能会在实验完成时产生更直接、更有效和更精确的分析；这项研究为几种重要的实验情况下的最优设计提供了数学结构。最优重复测量设计可以在对每个实验单元进行观察序列或计划对曲线进行集体分析时使用。对于许多情况下，最大的不确定性来源在于模型的初始选择，设计将被构建成对假设模型的偏差具有健壮性。对于一些非常理想的观测是不可能的或代价过高的情况，将使用组合和优化理论来开发标准和算法，以便在“接近最佳”的设计中进行选择。

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.