Constructions for Nonstationary Spatial Processes

Authored by: Paul D. Sampson

Handbook of Spatial Statistics

Print publication date:  March  2010
Online publication date:  March  2010

Print ISBN: 9781420072877
eBook ISBN: 9781420072884
Adobe ISBN:

10.1201/9781420072884-c9

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Abstract

Modeling of the spatial dependence structure of environmental processes is fundamental to almost all statistical analyses of data that are sampled spatially. The classical geostatistical model for a spatial process (Y(s) : s ∊ D} defined over the spatial domain D ⊂ ℝ d , specifies a decomposition into mean (or trend) and residual fields, Y(s) = μ( s ) + e(s). The process is commonly assumed to be second order stationary, meaning that the spatial covariance function can be written C (s, s+h) = Cov(Y(s), Y(s+h)) = Cov(e (s), e (s+h)) = C (h),sothat the covariance between any two locations depends only on the spatial lag vector connecting them. There is a long history of modeling the spatial covariance under an assumption of “intrinsic stationarity” in terms of the semivariogram, γ (h) = 1 2 var( Y(s+h) −Y(s)). However, it is now widely recognized that most, if not all, environmental processes manifest spatially nonstationary or heterogeneous covariance structure when considered over sufficiently large spatial scales.

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