{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T16:28:44Z","timestamp":1790872124162,"version":"4.1.0"},"reference-count":0,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2001,7,1]],"date-time":"2001-07-01T00:00:00Z","timestamp":993945600000},"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":[[2001,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We propose a two-stage algorithm for computing maximum likelihood estimates for a class of spatial models. The algorithm combines Markov chain Monte Carlo methods such as the Metropolis\u2013Hastings\u2013Green algorithm and the Gibbs sampler, and stochastic approximation methods such as the off-line average and adaptive search direction. A new criterion is built into the algorithm so stopping is automatic once the desired precision has been set. Simulation studies and applications to some real data sets have been conducted with three spatial models. We compared the algorithm proposed with a direct application of the classical Robbins\u2013Monro algorithm using Wiebe's wheat data and found that our procedure is at least 15 times faster.<\/jats:p>","DOI":"10.1111\/1467-9868.00289","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:36:38Z","timestamp":1047497798000},"page":"339-355","source":"Crossref","is-referenced-by-count":74,"title":["Maximum Likelihood Estimation for Spatial Models by Markov Chain Monte Carlo Stochastic Approximation"],"prefix":"10.1093","volume":"63","author":[{"given":"Ming Gao","family":"Gu","sequence":"first","affiliation":[{"name":"Chinese University of Hong Kong , People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong-Tu","family":"Zhu","sequence":"additional","affiliation":[{"name":"University of Victoria , Canada"}],"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%2F1467-9868.00289","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00289","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/63\/2\/339\/49590426\/jrsssb_63_2_339.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/63\/2\/339\/49590426\/jrsssb_63_2_339.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T09:44:39Z","timestamp":1679478279000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/63\/2\/339\/7083356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,7,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2002,1,6]]},"published-print":{"date-parts":[[2001,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00289","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2001,7]]},"published":{"date-parts":[[2001,7,1]]}}}