Space-Time Variograms and Covariance Models

时空变异函数和协方差模型

• 批准号: 0604942
• 负责人: Chunsheng Ma
• 金额: $ 12万
• 依托单位: Wichita State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-15 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604942&HistoricalAwards=false
• 关键词: Space; Time; Variograms; Covariance; Models

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.

研究者研究了各种时空随机场，包括高斯随机场，非高斯随机场和泊松点过程，并使用变异函数和协方差函数作为主要工具来描述时空相互作用和依赖。该项目的目的是提供构建非高斯随机场的宝贵技术;引入具有灵活性和物理可解释性的新的时空变异函数和协方差模型;研究其重要特性，以便从业者更容易选择具有有效和高效实际用途的适当模型;开发算法上有效的方法，用这种变差函数和协方差函数模拟时空随机场;对模型进行适当的统计推断;世界是一个多时空尺度的动态世界，时空相互作用在环境科学、信息科学和地球物理科学的各个领域都是普遍存在的。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，月份，日期等）的变化造成的。一个人的健康可能会受到他/她在一段时间内居住的地方的影响。国土安全方面的现象也随着时间和空间的变化而变化。该项目在不同领域具有潜在的应用，例如在大气科学、环境科学、地球物理科学、农业、生物学、健康和医学、水文学等方面的应用。它的成功不仅会影响统计建模的领域，而且有助于推进应用领域的研究。