Modeling and Prediction of Nonstationary Spatial Environmental Processes

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Title: Modeling and Prediction of Nonstationary Spatial Environmental Processes
Author: Barber, Jarrett Jay
Advisors: Montserrat Fuentes, Committee Chair
Peter Bloomfield, Committee Member
Jerry M. Davis, Committee Member
Marc G. Genton, Committee Member
Marcia L. Gumpertz, Committee Member
Abstract: Spatial data are often collected for the purpose of producing spatial predictions (i.e., maps), the accuracy of which relies on a good estimate of the spatial covariance. Traditional geostatistical methods for spatial interpolation assume covariance stationarity. However, spatial data often exhibit nonstationary covariance, and traditional methods can produce maps that are misleading. Some existing approaches to nonstationarity feature process models which lead naturally to a globally defined covariance but do not retain a familiar interpretation in terms of local stationarity, while other approaches focus on local stationarity but rely on ad hoc methods for calculating covariance. We present a different approach with a relatively simple but useful model for space-time data. The model is simultaneously defined everywhere (globally) and leads immediately to a globally defined covariance, and, locally, the model behaves like a stationary process. A nonparametric approach to estimating the nonstationary spatial covariance is presented along with some asymptotic properties. The approach is particularly suited to time-rich, spatially-sparse networks. We illustrate this nonparametric approach for spatial prediction of atmospheric pollution data collected periodically from an EPA environmental monitoring network. We also propose an alternative, parametric approach to estimation and prediction using a Bayesian formulation of a nonstationary spatial model.
Date: 2002-08-19
Degree: PhD
Discipline: Statistics

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