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

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M. FUENTES: DMS - 0353029 ABSTRACTClassical geostatistics and Fourier spectral methods are powerfultools to study the spatial temporal structure of stationary andseparable processes. However, it is widely recognized that in realapplications spatial temporal processes are rarely stationary andseparable. Thus an important extension of these spectral methods is toprocesses that are nonstationary and nonseparable. In this work, theinvestigator presents some new spectral approaches and tools toestimate, model, and test for nonstationarity and nonseparability.The investigator introduces nonparametric approaches and fittingalgorithms to estimate the spatial temporal structure of anonstationary and nonseparable spatial process defined on a continuousspace, and studies the asymptotic properties of these estimates. Themethods are based on a spectral approach, using spectral functionsthat are space-time dependent. The most important scientificcontributions of the research proposed here are: the parametric andnonparametric estimation of the complex spatial temporal dependence ofenvironmental processes in general situations (nonstationarity,anisotropy, nonseparability); the introduction of flexible models forspatial prediction of environmental processes using spectral methods;and new methodology for spatial prediction and estimation in thepresence of massive data.Spatial processes are an important modeling tool for manyenvironmental and scientific problems. Environmental scientists whowork with spatial temporal data, however, do not typically believethat real data satisfy the simple model assumptions such asseparability and stationarity that are currently used in practice.Therefore, it is is imperative for statisticians to develop methodswithout using those assumptions, especially for use with massivespatial-temporal (environmental) data sets. Through collaborationswith scientists, the new statistical models and methods proposed bythe investigator for estimation and prediction of space-timeprocesses, will enhance science by improving weather and air qualitymapping. The investigator will develop applications in collaborationwith atmospheric scientists and oceanographers on data assimilationproblems and on assessment of the performance of weather, ocean, andair quality numerical models. The methods proposed here for spacetime processes are also applicable to other fields. Past interactionsof the PI with various scientists at the Environmental ProtectionAgency (EPA), the National Oceanic and Atmospheric Administration(NOAA), and the National Center for Atmospheric Research (NCAR) areevidence that previous work of the PI has had an impact on variousfields. At NCSU there is ahigh proportion of women, American and African-American studentscompared to other Statistics departments. Five out of the seven PhDstudents currently working on their dissertations under the PI'ssupervision are women. The PI will continue her efforts to broaden theparticipation of minorities and women.