ABSTRACT
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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 O(n3) operations. The spectral version of the Gaussian log likelihood for gridded data requires O(nlog2n) operations and does not involve calculating determinants.
