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Covariance structure of spatial and spatiotemporal processes

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An important aspect of statistical modeling of spatial or spatiotemporal data is to determine the covariance function. It is a key part of spatial prediction (kriging). The classical geostatistical approach uses an assumption of isotropy, which yields circular isocorrelation curves. However, this is inappropriate for many applications, and several nonstationary approaches have been developed. Adding the temporal aspect, there is often interaction between time and space, requiring classes of nonseparable covariance structures. WIREs Comput Stat 2013, 5:279–287. doi: 10.1002/wics.1259 This article is categorized under: Data: Types and Structure > Image and Spatial Data Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Space–time covariance of ozone concentrations in an area around Sacramento, California, as a function of diurnal hour. In each pair the left figure is the deformation, and the right figure the estimated covariance in the deformed space. (Reprinted with permission from Ref . Copyright 1995 University of Washington)
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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Data: Types and Structure > Image and Spatial Data

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