Efficient and Robust Designs Based on Ordered Units

DMS-0204532PI：Dibyen Majudar标题：基于有序单元的高效而稳健的设计这个项目的目标是为随着时间的推移而进行的实验找到有效的设计，以比较不同的处理、不同的对象或方法。该项目的很大一部分涉及交叉实验，在这种情况下，受试者经常在实验结束前辍学，从而减少数据的信息含量，甚至危及结论的有效性。这里的目的是确定在很大程度上对受试者辍学具有健壮性的高效设计。该项目的另一部分涉及实验，其中随时间的趋势必须在模型和分析中考虑在内。这里的目的是确定足够灵活的有效设计，以适应实际应用中出现的各种实验条件和模型。适当的统计设计是科学实验的关键方面；它确保基于观察数据的结论在更大的背景下仍然有效。这个项目涉及各种领域的实验，包括生物医学、农业和工业实验，这些实验是随着时间的推移而进行的。随着实验的进行，不可控因素可能会影响结果。这个项目的目的是开发在不同的实验条件下表现良好的设计，以及在实验结束前对实验对象的无意损失具有健壮性的设计。

AbstractDMS-0204532PI: Dibyen MajumdarTitle: Efficient and Robust Designs Based on Ordered UnitsThe goal of this project is to find efficient designs for experiments conducted over time to compare different treatments, varieties of objects or methods. A substantial part of the project deals with crossover experiments, where it often happens that subjects drop out prior to the conclusion of the experiment, thereby reducing the information content of the data, or even jeopardizing the validity of the conclusions. Here the aim is to identify efficient designs that are largely robust to subject dropout. Another part of the project deals with experiments where a trend over time must be accounted for in the model and analysis. Here the aim is to identify efficient designs that are flexible enough to accommodate a wide variety of experimental conditions and models that arise in real applications.Proper statistical design is a critical aspect of scientific experiments; it ensures that the conclusions, based on observed data, remain valid in the larger context. This project deals with experiments in a variety of fields, including biomedical, agricultural and industrial experiments, that are conducted over time. As the experiment progresses, uncontrollable factors could influence the outcome. The aim of this project is to develop designs that perform well in diverse experimental conditions as well as designs that are robust against the inadvertent loss of experimental subjects before the conclusion of the experiment.