{"id":"https://openalex.org/W2014125835","doi":"https://doi.org/10.1198/106186006x128551","title":"Fast and Exact Simulation of Large Gaussian Lattice Systems in \u211d2: Exploring the Limits","display_name":"Fast and Exact Simulation of Large Gaussian Lattice Systems in \u211d2: Exploring the Limits","publication_year":2006,"publication_date":"2006-09-01","ids":{"openalex":"https://openalex.org/W2014125835","doi":"https://doi.org/10.1198/106186006x128551","mag":"2014125835"},"language":"en","primary_location":{"id":"doi:10.1198/106186006x128551","doi":"https://doi.org/10.1198/106186006x128551","is_oa":false,"landing_page_url":"https://doi.org/10.1198/106186006x128551","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046150465","display_name":"Tilmann Gneiting","orcid":"https://orcid.org/0000-0001-9397-3271","observed_orcids":["https://orcid.org/0000-0001-9397-3271"]},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Tilmann Gneiting","raw_affiliation_strings":["Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","institution_ids":["https://openalex.org/I190134885","https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077243781","display_name":"Hana \u0160ev\u010d\u00edkov\u00e1","orcid":"https://orcid.org/0000-0001-8674-0410","observed_orcids":["https://orcid.org/0000-0001-8674-0410","https://orcid.org/0000-0003-3718-474X","https://orcid.org/0000-0002-7896-1704"]},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Hana \u0160ev\u010d\u00edkov\u00e1","raw_affiliation_strings":["Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","institution_ids":["https://openalex.org/I190134885","https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037636060","display_name":"Donald B. Percival","orcid":"https://orcid.org/0000-0002-4732-477X","observed_orcids":["https://orcid.org/0000-0002-4732-477X"]},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Donald B Percival","raw_affiliation_strings":["Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","institution_ids":["https://openalex.org/I190134885","https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067826911","display_name":"Martin Schlather","orcid":"https://orcid.org/0000-0002-6919-7249","observed_orcids":["https://orcid.org/0000-0002-6919-7249"]},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Martin Schlather","raw_affiliation_strings":["Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","Helmut\u2010Schmidt\u2010University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","institution_ids":["https://openalex.org/I190134885","https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"raw_affiliation_string":"Helmut\u2010Schmidt\u2010University","institution_ids":["https://openalex.org/I190134885"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051311503","display_name":"Yindeng Jiang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Yindeng Jiang","raw_affiliation_strings":["Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilmann Gneiting is Associate Professor, Hana \u0160ev\u010d\u00edkov\u00e1 is Research Associate, and Yindeng Jiang is Graduate Research Assistant, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. Donald B. Percival is Principal Mathematician at the Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640. Martin Schlather is Associate Professor at Helmut-Schmidt-Universit\u00e4t, Institut f\u00fcr Statistik und Quantitative \u00d6konomik, Postfach 700822, 22008 Hamburg, Germany (E-mail for correspondence:","institution_ids":["https://openalex.org/I190134885","https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.69,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.95872791,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"15","issue":"3","first_page":"483","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.5957000255584717,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.5957000255584717,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.17829999327659607,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.09030000120401382,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-embedding","display_name":"circulant embedding","score":0.8550000190734863},{"id":"https://openalex.org/keywords/exact-simulation","display_name":"exact simulation","score":0.9810000061988831},{"id":"https://openalex.org/keywords/gaussian-random-fields","display_name":"Gaussian random fields","score":0.921999990940094},{"id":"https://openalex.org/keywords/stationary-random-fields","display_name":"stationary random fields","score":0.6209999918937683},{"id":"https://openalex.org/keywords/covariance-function","display_name":"covariance function","score":0.460999995470047},{"id":"https://openalex.org/keywords/matern-covariance-function","display_name":"Mat\u00e9rn covariance","score":0.8119999766349792},{"id":"https://openalex.org/keywords/large-scale-simulation","display_name":"large-scale simulation","score":0.38999998569488525}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7295045256614685},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.6641949415206909},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.660491943359375},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6489813923835754},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5634574890136719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5235804319381714},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.514167070388794},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.48658430576324463},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4682748317718506},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46704405546188354},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4620164632797241},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4349171221256256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39006122946739197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2933827340602875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2639642655849457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2607838213443756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2593398988246918},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1387610137462616},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11623609066009521},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07867273688316345},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1198/106186006x128551","doi":"https://doi.org/10.1198/106186006x128551","is_oa":false,"landing_page_url":"https://doi.org/10.1198/106186006x128551","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W55912154","https://openalex.org/W143236119","https://openalex.org/W161521922","https://openalex.org/W1555994268","https://openalex.org/W1720541938","https://openalex.org/W1964223342","https://openalex.org/W1967639991","https://openalex.org/W1967924750","https://openalex.org/W1968414728","https://openalex.org/W1969761972","https://openalex.org/W1971597992","https://openalex.org/W1981745143","https://openalex.org/W1982575727","https://openalex.org/W1996007769","https://openalex.org/W2005317633","https://openalex.org/W2017769677","https://openalex.org/W2019371791","https://openalex.org/W2024952168","https://openalex.org/W2027792629","https://openalex.org/W2035018697","https://openalex.org/W2037942041","https://openalex.org/W2060504103","https://openalex.org/W2062446895","https://openalex.org/W2076204683","https://openalex.org/W2079321251","https://openalex.org/W2079559649","https://openalex.org/W2110906205","https://openalex.org/W2130761473","https://openalex.org/W2153700325","https://openalex.org/W2167943787","https://openalex.org/W2168464387","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2051374412","https://openalex.org/W2079559649","https://openalex.org/W1901745588","https://openalex.org/W3172903033","https://openalex.org/W2809069633","https://openalex.org/W4298784191","https://openalex.org/W2325530052","https://openalex.org/W4286962214","https://openalex.org/W2394909248","https://openalex.org/W2466539766"],"abstract_inverted_index":{"The":[0,19,87],"circulant":[1],"embedding":[2,38],"technique":[3],"allows":[4],"for":[5,48,82,103],"the":[6,27,36,46],"fast":[7,28],"and":[8,13,24,80,99,114],"exact":[9,32,90],"simulation":[10],"of":[11,92,106],"stationary":[12,15],"intrinsically":[14],"Gaussian":[16,94],"random":[17],"fields.":[18],"method":[20,88],"uses":[21],"periodic":[22,37,63],"embeddings":[23,64],"relies":[25],"on":[26,66],"Fourier":[29],"transform.":[30],"However,":[31],"simulations":[33,91],"require":[34],"that":[35],"is":[39,43,75,85],"nonnegative":[40,61],"definite,":[41],"which":[42],"frequently":[44],"not":[45],"case":[47],"two-dimensional":[49],"simulations.":[50],"This":[51],"work":[52],"considers":[53],"a":[54],"suggestion":[55],"by":[56],"Michael":[57],"Stein,":[58],"who":[59],"proposed":[60],"definite":[62],"based":[65],"suitably":[67],"modified,":[68],"compactly":[69],"supported":[70],"covariance":[71],"functions.":[72],"Theoretical":[73],"support":[74],"given":[76],"to":[77],"this":[78],"proposal,":[79],"software":[81],"its":[83],"implementation":[84],"provided.":[86],"yields":[89],"planar":[93],"lattice":[95,101],"systems":[96],"with":[97,110],"106":[98],"more":[100],"points":[102],"wide":[104],"classes":[105],"processes,":[107],"including":[108],"those":[109],"powered":[111],"exponential,":[112],"Mat\u00e9rn,":[113],"Cauchy":[115],"covariances.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}