{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:45:21Z","timestamp":1768409121972,"version":"3.49.0"},"reference-count":12,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T00:00:00Z","timestamp":1615507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,5,25]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We conduct a study of the aliased spectral densities of Mat\u00e9rn covariance functions on a regular grid of points, elucidating the properties of a popular approximation based on stochastic partial differential equations. While other researchers have shown that this approximation can work well for the covariance function, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.<\/jats:p>","DOI":"10.1093\/biomet\/asab017","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T20:11:46Z","timestamp":1615320706000},"page":"535-541","source":"Crossref","is-referenced-by-count":5,"title":["Inverses of Mat\u00e9rn covariances on grids"],"prefix":"10.1093","volume":"109","author":[{"given":"Joseph","family":"Guinness","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Cornell University, 1178 Comstock Hall, Ithaca, New York 14853, U.S.A. guinness@cornell.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,3,12]]},"reference":[{"key":"2022052609543123400_B1","doi-asserted-by":"crossref","first-page":"e1443","DOI":"10.1002\/wics.1443","article-title":"Spatial modeling with R-INLA: A review","volume":"10","author":"Bakka,","year":"2018","journal-title":"WIREs Comp. Statist."},{"key":"2022052609543123400_B2","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1111\/j.2517-6161.1981.tb01675.x","article-title":"On a system of two-dimensional recurrence equations","volume":"43","author":"Besag,","year":"1984","journal-title":"J. R. Statist. Soc. B"},{"key":"2022052609543123400_B3","first-page":"115","article-title":"Exploring a new class of non-stationary spatial Gaussian random fields with varying local anisotropy","volume":"25","author":"Fuglstad,","year":"2015","journal-title":"Statist. Sinica"},{"key":"2022052609543123400_B4","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1080\/00401706.2018.1437476","article-title":"Permutation and grouping methods for sharpening Gaussian process approximations","volume":"60","author":"Guinness,","year":"2018","journal-title":"Technometrics"},{"key":"2022052609543123400_B5","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1093\/biomet\/93.4.989","article-title":"Studies in the history of probability and statistics XLIX: On the Matern correlation family","volume":"93","author":"Guttorp,","year":"2006","journal-title":"Biometrika"},{"key":"2022052609543123400_B6","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1111\/j.1467-9868.2011.00777.x","article-title":"An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach","volume":"73","author":"Lindgren,","year":"2011","journal-title":"J. R. Statist. Soc. B"},{"key":"2022052609543123400_B7","author":"R Development Core Team","year":"2022","journal-title":"R: A Language and Environment for Statistical Computing"},{"key":"2022052609543123400_B8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1494-6","volume-title":"Interpolation of Spatial Data: Some Theory for Kriging","author":"Stein,","year":"1999"},{"key":"2022052609543123400_B9","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1111\/j.2517-6161.1988.tb01729.x","article-title":"Estimation and model identification for continuous spatial processes","volume":"50","author":"Vecchia,","year":"1988","journal-title":"J. R. Statist. Soc. B"},{"key":"2022052609543123400_B10","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1093\/biomet\/41.3-4.434","article-title":"On stationary processes in the plane","volume":"41","author":"Whittle,","year":"1954","journal-title":"Biometrika"},{"key":"2022052609543123400_B11","first-page":"974","article-title":"Stochastic processes in several dimensions","volume":"40","author":"Whittle,","year":"1963","journal-title":"Bull. Int. Statist. Inst."},{"key":"2022052609543123400_B12","volume-title":"Gaussian Processes for Machine Learning","author":"Williams,","year":"2006"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asab017\/39771188\/asab017.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/2\/535\/43832436\/asab017.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/2\/535\/43832436\/asab017.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,25]],"date-time":"2024-08-25T18:48:53Z","timestamp":1724611733000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/109\/2\/535\/6168989"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,12]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,3,12]]},"published-print":{"date-parts":[[2022,5,25]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asab017","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,6,1]]},"published":{"date-parts":[[2021,3,12]]}}}