Spectral Domain

Authored by: Montserrat Fuentes , Brian Reich

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-c5

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Abstract

Spectral methods are a powerful tool for studying the spatial structure of spatial continuous processes and sometimes offer significant computational benefits. Using the spectral representation of a spatial process we can easily construct valid (positive definite) covariance functions and introduce new models for spatial fields. Likelihood approaches for large spatial datasets are often very difficult, if not infeasible, to implement due to computational limitations. Even when we can assume normality, exact calculations of the likelihood for a Gaussian spatial process observed at n locations requires 0(n 3) operations. The spectral version of the Gaussian log likelihood for gridded data requires O(nlog 2 n) operations and does not involve calculating determinants.

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