Mathematical Sciences: Model Robust Design and Inference

数学科学：模型稳健设计和推理

• 批准号: 8703802
• 负责人: Jerome Sacks
• 金额: $ 8.46万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703802&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Model; Robust; Design

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.

这项研究将是在设置实验设计 允许系统偏离精确线性模型 但被控制住了 尺寸设计问题的研究 比一个更高的是通过控制 通过使用一个随机过程偏离先验。 有和没有测量误差的问题是感兴趣的。 与后一种情况相适应的重要而有趣的问题出现了 在数值积分和输入的选择， 计算机模型实验和模拟。 算法 计算设计是设计，研究和比较。 线性设计的预测将被设计、研究和 比较了 下式的线性泛函的预测 回归或过程将被强调;非线性泛函 带来了更多的问题，也需要研究。 的复杂性 问题和解决复杂设计空间的必要性 导致对高级计算资源的需要和使用。 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。 大多数当前 统计理论适用于非常简单的实验 和分析技术。 这是因为，直到计算机 革命，实验的可行性受到严重限制 通过数据收集和计算能力。 本研究 是拓宽实验设计的理论， 适用于更现代的科学环境， 这些进步使得更复杂的问题可以在 受控和对照实验。