文章基本信息

标题：On Circulant Embedding for Gaussian Random Fields in R
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作者：Tilman M. Davies ; David Bryant
期刊名称：Journal of Statistical Software
印刷版ISSN：1548-7660
电子版ISSN：1548-7660
出版年度：2013
卷号：55
期号：1
页码：1-21
语种：English
出版社：University of California, Los Angeles
摘要：The high-dimensionality typically associated with discretized approximations to Gaussian random fields is a considerable hinderance to computationally efficient methods for their simulation. Many direct approaches require spectral decompositions of the associated covariance matrix and so are unable to complete the solving process in a timely fashion, if at all. However under certain conditions, we may construct block-circulant versions of the covariance matrix at hand thereby allowing access to fast-Fourier methods to perform the required operations with impressive speed. We demonstrate how circulant embedding and subsequent simulation can be performed directly in the R language. The approach is currently implemented in C for the R package RandomFields , and used in the recently released package lgcp . Motivated by applications dealing with spatial point processes we restrict attention to stationary Gaussian fields on R 2 , where sparsity of the covariance matrix cannot necessarily be assumed.