{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T18:28:08Z","timestamp":1790620088666,"version":"4.1.0"},"reference-count":0,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2000,11,1]],"date-time":"2000-11-01T00:00:00Z","timestamp":973036800000},"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":[[2000,11,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Statistical space\u2013time modelling has traditionally been concerned with separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-separable covariance function. The model is well suited to a wide range of realistic problems which will be poorly fitted by separable models. The model operates successively in time: the spatial field at time t +1 is obtained by \u2018blurring\u2019 the field at time t and adding a spatial random field. The model is first introduced at discrete time steps, and the limit is taken as the length of the time steps goes to 0. This gives a consistent continuous model with parameters that are interpretable in continuous space and independent of sampling intervals. Under certain conditions the blurring must be a Gaussian smoothing kernel. We also show that the model is generated by a stochastic differential equation which has been studied by several researchers previously.<\/jats:p>","DOI":"10.1111\/1467-9868.00269","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:35:58Z","timestamp":1047497758000},"page":"847-860","source":"Crossref","is-referenced-by-count":108,"title":["Blur-generated non-separable space\u2013time models"],"prefix":"10.1093","volume":"62","author":[{"given":"Patrick E.","family":"Brown","sequence":"first","affiliation":[{"name":"Lancaster University , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gareth O.","family":"Roberts","sequence":"additional","affiliation":[{"name":"Lancaster University , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kjetil F.","family":"K\u00e5resen","sequence":"additional","affiliation":[{"name":"Norwegian Computing Centre , Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Tonellato","sequence":"additional","affiliation":[{"name":"Universit\u00e0 Ca' Foscari di Venezia , Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2002,1,6]]},"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00269","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/62\/4\/847\/49589766\/jrsssb_62_4_847.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/62\/4\/847\/49589766\/jrsssb_62_4_847.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T07:00:33Z","timestamp":1679468433000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/62\/4\/847\/7083259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,11,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2002,1,6]]},"published-print":{"date-parts":[[2000,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00269","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2000,11]]},"published":{"date-parts":[[2000,11,1]]}}}