Mathematical Sciences: Model Robust Design and Inference

这项研究将在允许但可控制系统偏离精确线性模型的环境下进行实验设计。通过使用随机过程先验来控制偏离，极大地促进了对维度高于1的设计问题的研究。有测量误差和无测量误差的问题是很重要的。与后一种情况相适应的重要而有趣的问题出现在数值积分以及计算机模型实验和模拟的输入选择中。计算设计的算法将被设计、研究和比较。线性设计的预测将被设计、研究和比较。将强调对潜在回归或过程的线性泛函的预测；非线性泛函也带来了需要研究的额外问题。问题的复杂性和解决复杂设计空间的必要性导致了对高级计算资源的需求和使用。统计实验设计的主要目标是评估拟议实验的可行性，并优化实验中的资源使用。目前的大多数统计理论都适用于结构非常简单的实验和分析技术。这是因为，在计算机革命之前，实验的可行性受到数据收集和计算能力的严重限制。这项研究是为了拓宽实验设计的理论，以便实际应用于更现代的科学环境，在这些环境中，技术进步允许在受控和受控实验中研究更复杂的问题。

This research will be on experimental designs in settings where systematic departures from exact linear models are allowed but controlled. The study of design problems in dimensions higher than one is facilitated greatly by controlling the departure through the use of a stochastic process prior. Problems with and without measurement error are of interest. Important and interesting problems fitting the latter case arise in numerical integration and in the selection of inputs to computer model experiments and simulations. Algorithms for computing designs are to be devised, studied, and compared. Prediction of linear designs are to be devised, studied and compared. Prediction of linear functionals of the underlying regression or process will be emphasized; non-linear functionals bring added concerns also requiring study. The complexity of the problems and the necessity for addressing complex design spaces leads to the need and use of advanced computational resources. The primary goal of statistical experimental design is to assess the feasibility of a proposed experiment and to optimize the use of resources in the experiment. Most of current statistical theory applies to very simply configured experiments and analysis techniques. This is so because, until the computer revolution, the feasibility of experiments were severely limited by data collection and computational capabilities. This research is to broaden the theory of experimental design, to realistically apply to more modern scientific settings where technological advances are permitting more complex questions to be studied in controlled and controlled experiments.