{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T01:58:19Z","timestamp":1793498299948,"version":"4.5.0"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2021,12,4]],"date-time":"2021-12-04T00:00:00Z","timestamp":1638576000000},"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":[[2022,11,29]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Mat\u00e9rn functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations scale up in quadratic and cubic order, respectively, with the number of variables. We propose a class of multivariate graphical Gaussian processes using a general construction called stitching that crafts cross-covariance functions from graphs and ensures process-level conditional independence between variables. For the Mat\u00e9rn family of functions, stitching yields a multivariate Gaussian process whose univariate components are Mat\u00e9rn Gaussian processes, and which conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Mat\u00e9rn Gaussian process to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.<\/jats:p>","DOI":"10.1093\/biomet\/asab061","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T20:12:40Z","timestamp":1638216760000},"page":"993-1014","source":"Crossref","is-referenced-by-count":25,"title":["Graphical Gaussian process models for highly multivariate spatial data"],"prefix":"10.1093","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2579-5693","authenticated-orcid":false,"given":"Debangan","family":"Dey","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health , 615 N. 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