{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T19:26:02Z","timestamp":1790882762970,"version":"4.1.0"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":6106,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for Promotion of Science","doi-asserted-by":"crossref","award":["P04039"],"award-info":[{"award-number":["P04039"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["EAR 0409890"],"award-info":[{"award-number":["EAR 0409890"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper gives first-order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by Baddeley and co-workers for spatial point processes and also proposes principles for second-order residual analysis based on the viewpoint of martingales. Examples are given for both first- and second-order residuals. In particular, residual analysis can be used as a powerful tool in model improvement. Taking a spatiotemporal epidemic-type aftershock sequence model for earthquake occurrences as the base-line model, second-order residual analysis can be useful for identifying many features of the data that are not implied in the base-line model, providing us with clues about how to formulate better models.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00559.x","type":"journal-article","created":{"date-parts":[[2006,7,19]],"date-time":"2006-07-19T16:08:38Z","timestamp":1153325318000},"page":"635-653","source":"Crossref","is-referenced-by-count":83,"title":["Second-Order Residual Analysis of Spatiotemporal Point Processes and Applications in Model Evaluation"],"prefix":"10.1093","volume":"68","author":[{"given":"Jiancang","family":"Zhuang","sequence":"first","affiliation":[{"name":"Institute of Statistical Mathematics , Tokyo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,7,19]]},"reference":[{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1111\/j.1467-9868.2005.00519.x","article-title":"Residual analysis for spatial point processes (with discussion)","volume":"67","author":"Baddeley","year":"2005","journal-title":"J. R. Statist. Soc. B"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9477-8","volume-title":"Point Processes and Queues: Martingale Dynamics","author":"Br\u00e9maud","year":"1981"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"8699","DOI":"10.1029\/2000JB900269","article-title":"A simple and testable model for earthquake clustering","volume":"106","author":"Console","year":"2001","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","first-page":"2468","DOI":"10.1029\/2002JB002130","article-title":"Refining earthquake clustering models","volume":"108","author":"Console","year":"2003","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","volume-title":"An Introduction to Theory of Point Processes","author":"Daley","year":"2003"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1785\/BSSA0460020105","article-title":"Earthquake magnitude, intensity, energy, and acceleration","volume":"46","author":"Gutenberg","year":"1956","journal-title":"Bull. Seism. Soc. Am."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","DOI":"10.1029\/2004JB003247","article-title":"Detecting fluid signals in seismicity data through statistical earthquake modeling","volume":"110","author":"Hainzl","year":"2005","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","first-page":"2457","DOI":"10.1029\/2003JB002409","article-title":"Foreshocks explained by cascades of triggered seismicity","volume":"108","author":"Helmstetter","year":"2003","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","first-page":"2482","DOI":"10.1029\/2003JB002485","article-title":"Predictability in the ETAS model of interacting triggered seismicity","volume":"108","author":"Helmstetter","year":"2003","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","first-page":"2046","DOI":"10.1029\/2002JB001991","article-title":"Mainshocks are aftershocks of conditional foreshocks: how do foreshock statistical properties emerge from aftershock laws","volume":"108","author":"Helmstetter","year":"2003","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1111\/j.1365-246X.1991.tb04607.x","article-title":"Likelihood analysis of earthquake catalogues","volume":"106","author":"Kagan","year":"1991","journal-title":"Geophys. J. Int."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1029\/JB086iB04p02853","article-title":"Stochastic synthesis of earthquake catalogs","volume":"86","author":"Kagan","year":"1981","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","volume-title":"Point Processes and Their Statistical Inference","author":"Karr","year":"1991","edition":"2nd"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/BFb0058859","article-title":"Demonstration simplifi\u00e9e d'un th\u00e9or\u00e8me de Knight","volume":"191","author":"Meyer","year":"1971","journal-title":"Lect. Notes Math."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00048666","article-title":"A space-time clustering model for historical earthquakes","volume":"44","author":"Musmeci","year":"1992","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1002\/mana.19790880109","article-title":"Integral and differential characterizations of the Gibbs process","volume":"88","author":"Nguyen","year":"1979","journal-title":"Math. Nacht."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/TIT.1981.1056305","article-title":"On Lewis\u2019 simulation method for point processes","volume":"27","author":"Ogata","year":"1981","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/01621459.1988.10478560","article-title":"Statistical model for earthquake occurrences and residual analysis for point processes","volume":"83","author":"Ogata","year":"1988","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1023\/A:1003403601725","article-title":"Space-time point-process models for earthquake occurrences","volume":"50","author":"Ogata","year":"1998","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","DOI":"10.1029\/2003JB002621","article-title":"Space-time model for regional seismicity and detection of crystal stress changes","volume":"109","author":"Ogata","year":"2004","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","first-page":"499","article-title":"Modelling heterogeneous space\u2013time occurrences of earthquakes and its residual analysis","volume":"52","author":"Ogata","year":"2003","journal-title":"Appl. Statist."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.tecto.2005.10.016","article-title":"Space-time ETAS models and an improved extension","volume":"413","author":"Ogata","year":"2006","journal-title":"Tectonophysics"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0002-9947-1972-0314102-9","article-title":"Integrability of expected increments point processes and a related random change of scale","volume":"165","author":"Papangelou","year":"1972","journal-title":"Trans. Mer. Math. Soc."},{"key":"2023040800095630800_","first-page":"379","article-title":"Modelling marked spatio-temporal point patterns","volume":"55","author":"Rathbun","year":"1993","journal-title":"Bull. Int. Statist. Inst."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1198\/016214503000000710","article-title":"Multidimensional residual analysis of point process models for earthquake occurrences","volume":"98","author":"Schoenberg","year":"2004","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1093\/biomet\/64.1.29","article-title":"Asymptotics for and against cross-validation","volume":"64","author":"Stone","year":"1977","journal-title":"Biometrika"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/mana.19911510108","article-title":"Second-order characteristics for stochastic structures connected with Gibbs point processes","volume":"151","author":"Stoyan","year":"1991","journal-title":"Math. Nacht."},{"key":"2023040800095630800_","first-page":"129","article-title":"Aftershock and earthquake statistics (I): Some parameters which characterize an aftershock sequence and their interrelations","volume":"3","author":"Utsu","year":"1969","journal-title":"J. Fac. Sci. Hokkaido Univ. VII"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1111\/j.1467-842X.2004.00319.x","article-title":"Rescaling marked point processes","volume":"46","author":"Vere-Jones","year":"2004","journal-title":"Aust. New Zeal. J. Statist."},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.4294\/jpe1952.38.305","article-title":"Scaling relationship between the number of aftershocks and the size of the main shock","volume":"38","author":"Yamanaka","year":"1990","journal-title":"J. Phys. Earth"},{"key":"2023040800095630800_","doi-asserted-by":"publisher","DOI":"10.1029\/2004JB003157","article-title":"A study on the background and clustering seismicity in the Taiwan region by using a point-process model","volume":"110","author":"Zhuang","year":"2005","journal-title":"J. Geophys. Res."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","DOI":"10.1103\/73.046134","article-title":"Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks","volume":"73","author":"Zhuang","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023040800095630800_","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1198\/016214502760046925","article-title":"Stochastic declustering of space-time earthquake occurrences","volume":"97","author":"Zhuang","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800095630800_","doi-asserted-by":"publisher","DOI":"10.1029\/2003JB002879","article-title":"Analyzing earthquake clustering features by using stochastic reconstruction","volume":"109","author":"Zhuang","year":"2004","journal-title":"J. Geophys. Res."}],"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%2Fj.1467-9868.2006.00559.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/4\/635\/49796569\/jrsssb_68_4_635.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/4\/635\/49796569\/jrsssb_68_4_635.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T04:30:32Z","timestamp":1683520232000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/68\/4\/635\/7110610"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,19]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2006,7,19]]},"published-print":{"date-parts":[[2006,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2006.00559.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2006,9]]},"published":{"date-parts":[[2006,7,19]]}}}