Estimation, Modeling and Prediction of Nonseparable and Nonstationary Space-Time Processes

North Carolina State University, Raleigh NC

Investigators

Abstract

M. FUENTES: DMS - 0353029 ABSTRACT Classical geostatistics and Fourier spectral methods are powerful tools to study the spatial temporal structure of stationary and separable processes. However, it is widely recognized that in real applications spatial temporal processes are rarely stationary and separable. Thus an important extension of these spectral methods is to processes that are nonstationary and nonseparable. In this work, the investigator presents some new spectral approaches and tools to estimate, model, and test for nonstationarity and nonseparability. The investigator introduces nonparametric approaches and fitting algorithms to estimate the spatial temporal structure of a nonstationary and nonseparable spatial process defined on a continuous space, and studies the asymptotic properties of these estimates. The methods are based on a spectral approach, using spectral functions that are space-time dependent. The most important scientific contributions of the research proposed here are: the parametric and nonparametric estimation of the complex spatial temporal dependence of environmental processes in general situations (nonstationarity, anisotropy, nonseparability); the introduction of flexible models for spatial prediction of environmental processes using spectral methods; and new methodology for spatial prediction and estimation in the presence of massive data. Spatial processes are an important modeling tool for many environmental and scientific problems. Environmental scientists who work with spatial temporal data, however, do not typically believe that real data satisfy the simple model assumptions such as separability and stationarity that are currently used in practice. Therefore, it is is imperative for statisticians to develop methods without using those assumptions, especially for use with massive spatial-temporal (environmental) data sets. Through collaborations with scientists, the new statistical models and methods proposed by the investigator for estimation and prediction of space-time processes, will enhance science by improving weather and air quality mapping. The investigator will develop applications in collaboration with atmospheric scientists and oceanographers on data assimilation problems and on assessment of the performance of weather, ocean, and air quality numerical models. The methods proposed here for space time processes are also applicable to other fields. Past interactions of the PI with various scientists at the Environmental Protection Agency (EPA), the National Oceanic and Atmospheric Administration (NOAA), and the National Center for Atmospheric Research (NCAR) are evidence that previous work of the PI has had an impact on various fields. At NCSU there is a high proportion of women, American and African-American students compared to other Statistics departments. Five out of the seven PhD students currently working on their dissertations under the PI's supervision are women. The PI will continue her efforts to broaden the participation of minorities and women.