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.
