Nonstationary covariance models

Montserrat Fuentes and Peter Guttorp
North Carolina State University and University of Washington

Spatial processes are an important modeling tool for many problems faced in the Earth sciences. Classical geostatistics is based on processes which are stationary and isotropic, but it is widely recognized that real environmental and geophysical processes are rarely stationary and isotropic. In this presentation we review the current methods available to analyze nonstationary spatial data. We present deformation approaches, EOFs, basis expansions covariance, kernel convolutions, and methods based on moving-windows. A class of nonstationary processes is also proposed, based on a convolution of local stationary processes. This model has the advantage that is simultaneously defined everywhere, unlike "moving window" approaches, but it retains the attractive property that locally in small regions, it behaves like a stationary spatial process.

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