Space-Time Variograms and Covariance Models

研究者研究了多种时空随机场，包括高斯随机场、非高斯随机场和泊松点过程，并使用变差函数和协方差函数作为描述时空相互作用和依赖性的主要工具。该项目的目的是为构造非高斯随机场提供有价值的技术；引入新的具有灵活性和物理可解释性的时空变异函数和协方差模型；研究它们的重要性质，以便从业者更容易选择具有实际应用效果的合适模型；开发算法高效的方法来模拟时空随机场与这些变量和协方差函数；对模型进行适当的统计推断；并将所建立的模型应用于各种实际案例，以证明所建立模型的实用性。世界在空间和时间的许多尺度上都是动态的，时空相互作用在环境科学、信息科学和地球物理科学的几乎每个领域都很普遍。例如，环境或全球变化的不确定性主要是由于地球物理位置在不同时间（季节、月、日等）的变化。一个人的健康可能受到他/她长期居住的地方的影响。国土安全现象也随着时间和空间的变化而变化。该项目在大气科学、环境科学、地球物理科学、农业、生物、卫生医学、水文学等领域具有广泛的应用前景。它的成功将不仅影响统计建模领域，而且有助于推进应用领域的研究。

The investigator studies a variety of space-time random fields, including Gaussian random fields, non-Gaussian random fields, and Poisson point processes, and uses variograms and covariance functions as main tools to describe space-time interaction and dependence. The aims of the project are to provide valuable techniques for constructing non-Gaussian random fields; to introduce new spatio-temporal variograms and covariance models with flexibility and physical interpretablity; to investigate their important properties so that practitioners would more easily choose appropriate models with effective and efficient practical usage; to develop algorithmically efficient methods for simulating space-time random fields with such variograms and covariance functions; to perform suitable statistical inference of the models; and to demonstrate the practicality of the developed models by applying our models to various practical cases.The world is dynamic at many scales in space and time, and the space-time interaction is prevalent in almost every field in the environmental, informational, and geophysical sciences. For example, uncertainty of environment or global change mostly results from variability of geophysical locations at different times (season, month, day, etc.). A human being's health may be affected by where s/he lives over periods of time. Phenomena in homeland security also evolve over space and time. This project has the potential applications in diverse fields, such as applications in atmospheric science, environmental science, geophysical science, agriculture, biology, health and medicine, hydrology, and others. Its success would impact not only the realm of statistical modeling, but also help advance research in the fields of the applications.