Simulation of stationary Gaussian vector fields

Authors:
G. Chan;A. T. A. Wood
Affiliations:
Department of Statistics, School of Mathematics, University of New South Wales, Sydney 2052, Australia;School of Mathematical Sciences, University of Bath, BA2 7AY, UK
Venue:
Statistics and Computing
Year:
1999

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Abstract

In earlier work we described a circulant embedding approach for simulating scalar-valued stationary Gaussian random fields on a finite rectangular grid, with the covariance function prescribed. Here, we explain how the circulant embedding approach can be used to simulate Gaussian vector fields. As in the scalar case, the simulation procedure is theoretically exact if a certain non-negativity condition is satisfied. In the vector setting, this exactness condition takes the form of a nonnegative definiteness condition on a certain set of Hermitian matrices. The main computational tool used is the Fast Fourier Transform. Consequently, when implemented appropriately, the procedure is highly efficient, in terms of both CPU time and storage.