Optimal Design of Experiments for Correlated Observations

摘要：对于独立观测的最优实验设计，人们已经做了大量的研究，而对于相关观测，仍然有许多具有挑战性的问题有待解决。研究人员开发了量化相关观测的复杂模型的不确定性的最优性标准，包括空间高斯和非高斯随机场模型和极值过程。算法的基础上，新开发的优化技术和扩展的设计措施，相关的意见进行了研究。该研究的智力价值是设计的新理论，方法和计算技术，特别是空间和时空设计，其中观测之间的相关性不容忽视。这包括量化空间预测中的不确定性的理论，使用二次和半定规划的设计算法，以及定义相关观测的设计度量的新方法及其在时空设计中的应用。研究人员研究如何最佳地放置监测器的问题，以便能够进行最准确的预测。这项工作的直接动机来自环境科学，其中网络用于监测污染物。众所周知，空气污染与人类健康有关，本提案中开发的方法可以帮助研究人员量化污染估计中的不确定性，这可能有助于更好地了解污染与人类健康之间的关系。特别是与环境保护局研究人员的互动可能会改善对大气污染物的监测。调查人员还打算研究生物监测项目的可能应用，该项目提供了一个生物威胁预警系统。这项研究的影响不仅限于环境科学，因为方法和算法原则上适用于许多其他领域，如气候学和化学动力学模型。

ABSTRACT:Much research has been done on the optimal design of experiments for independent observations, while for correlated observations there are still many challenging problems that remain to be solved. The investigators develop optimality criteria which quantify the uncertainty for complex models of correlated observations, including spatial Gaussian and non-Gaussian random field models and extreme value processes. Algorithms based on newly developed optimization techniques and extensions of design measures to correlated observations are investigated as well. The intellectual merit of the research is new theory, methodology, and computational techniques for design, in particular spatial and space-time designs where the correlations between observations cannot be ignored. This includes theories for quantifying uncertainties in spatial prediction, design algorithms using quadratic and semidefinite programming, and novel ways of defining design measure for correlated observations and their application in space-time design.In many applications, data are collected from a network of monitors in space and time to make predictions. The investigators study the problem of how to optimally place the monitors so that one can have the most accurate prediction. The direct motivation of this work is from environmental science, where networks are used to monitor the pollutants. Air pollution is known to be associated with human health, and the methods developed in this proposal can help researchers quantify the uncertainties in the pollution estimates, which may contribute to better understanding of the association between pollution and human health. In particular interactions with EPA researchers may lead to improved monitoring of atmospheric pollutants. The investigators also intend to study possible applications to Project BioWatch, which provides an early warning system for bio-threats. The impact of this research is not limited to the environmental science, as the methods and algorithm are in principle applicable to many other fields such as climatology and chemical kinetic models.