Space-Time Variograms and Covariance Models

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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.