{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T15:36:59Z","timestamp":1767713819217,"version":"3.37.3"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T00:00:00Z","timestamp":1544659200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000765","name":"University College London","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000765","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s11222-018-9845-z","type":"journal-article","created":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T11:45:34Z","timestamp":1544701534000},"page":"915-931","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Inference for ETAS models with non-Poissonian mainshock arrival times"],"prefix":"10.1007","volume":"29","author":[{"given":"Aleksandar A.","family":"Kolev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gordon J.","family":"Ross","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"issue":"2","key":"9845_CR1","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1162\/08997660252741149","volume":"14","author":"EN Brown","year":"2002","unstructured":"Brown, E.N., Barbieri, R., Ventura, V., Kass, R.E., Frank, L.M.: The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput. 14(2), 325\u2013346 (2002)","journal-title":"Neural Comput."},{"issue":"3","key":"9845_CR2","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1007\/s11069-012-0496-7","volume":"69","author":"C-H Chen","year":"2013","unstructured":"Chen, C.-H., Wang, J.-P., Wu, Y.-M., Chan, C.-H., Chang, C.-H.: A study of earthquake inter-occurrence times distribution models in Taiwan. Nat. Hazards 69(3), 1335\u20131350 (2013)","journal-title":"Nat. Hazards"},{"issue":"1","key":"9845_CR3","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1080\/10618600.2017.1341324","volume":"27","author":"F Chen","year":"2018","unstructured":"Chen, F., Stindl, T.: Direct likelihood evaluation for the renewal hawkes process. J. Comput. Graph. Stat. 27(1), 119\u2013131 (2018)","journal-title":"J. Comput. Graph. Stat."},{"issue":"4","key":"9845_CR4","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00031305.1995.10476177","volume":"49","author":"S Chib","year":"1995","unstructured":"Chib, S., Greenberg, E.: Understanding the Metropolis\u2013Hastings algorithm. Am. Stat. 49(4), 327\u2013335 (1995)","journal-title":"Am. Stat."},{"key":"9845_CR5","first-page":"23","volume":"522","author":"WL Ellsworth","year":"1999","unstructured":"Ellsworth, W.L., Matthews, M.V., Nadeau, R.M., Nishenko, S.P., Reasenberg, P.A., Simpson, R.W.: A physically based earthquake recurrence model for estimation of long-term earthquake probabilities. US Geol. Surv. 522, 23 (1999)","journal-title":"US Geol. Surv."},{"key":"9845_CR6","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.2307\/2999632","volume":"66","author":"RF Engle","year":"1998","unstructured":"Engle, R.F., Russell, J.R.: Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica 66, 1127\u20131162 (1998)","journal-title":"Econometrica"},{"issue":"8","key":"9845_CR7","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1080\/14697688.2015.1032544","volume":"15","author":"V Filimonov","year":"2015","unstructured":"Filimonov, V., Sornette, D.: Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data. Quant. Finance 15(8), 1293\u20131314 (2015)","journal-title":"Quant. Finance"},{"key":"9845_CR8","volume-title":"Bayesian Data Analysis","author":"A Gelman","year":"2014","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, vol. 2. CRC Press, Boca Raton (2014)"},{"issue":"2","key":"9845_CR9","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1093\/ije\/dyt043","volume":"42","author":"G Hamra","year":"2013","unstructured":"Hamra, G., MacLehose, R., Richardson, D.: Markov chain Monte Carlo: an introduction for epidemiologists. Int. J. Epidemiol. 42(2), 627\u2013634 (2013)","journal-title":"Int. J. Epidemiol."},{"key":"9845_CR10","unstructured":"Hyndman, R.J.: Thoughts on the Ljung\u2013Box test. (2014) https:\/\/robjhyndman.com\/hyndsight\/ljung-box-test\/ . Accessed 4 Aug 2017"},{"issue":"3","key":"9845_CR11","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/S0040-1951(01)00084-1","volume":"338","author":"M Imoto","year":"2001","unstructured":"Imoto, M.: Application of the stress release model to the Nankai earthquake sequence, southwest Japan. Tectonophysics 338(3), 287\u2013295 (2001)","journal-title":"Tectonophysics"},{"issue":"3","key":"9845_CR12","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/0304-4149(79)90008-5","volume":"8","author":"V Isham","year":"1979","unstructured":"Isham, V., Westcott, M.: A self-correcting point process. Stoch. Process. Appl. 8(3), 335\u2013347 (1979)","journal-title":"Stoch. Process. Appl."},{"key":"9845_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/0471715816","volume-title":"Univariate Discrete Distributions","author":"NL Johnson","year":"2005","unstructured":"Johnson, N.L., Kemp, A.W., Kotz, S.: Univariate Discrete Distributions, vol. 444. Wiley, Hoboken (2005)"},{"key":"9845_CR14","unstructured":"Kagan, Y., Knopoff, L.: A stochastic model of earthquake occurrence. In: Proceedings of the Eighth International Conference on Earthquake Engineering, vol.1, pp. 295\u2013302 (1984)"},{"issue":"12","key":"9845_CR15","doi-asserted-by":"publisher","first-page":"6165","DOI":"10.1002\/2013JB010259","volume":"118","author":"T Kumazawa","year":"2013","unstructured":"Kumazawa, T., Ogata, Y.: Quantitative description of induced seismic activity before and after the 2011 Tohoku\u2013Oki earthquake by nonstationary ETAS models. J. Geophys. Res. Solid Earth 118(12), 6165\u20136182 (2013)","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"1","key":"9845_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/14697688.2015.1068442","volume":"16","author":"M Lallouache","year":"2016","unstructured":"Lallouache, M., Challet, D.: The limits of statistical significance of Hawkes processes fitted to financial data. Quant. Finance 16(1), 1\u201311 (2016)","journal-title":"Quant. Finance"},{"issue":"3","key":"9845_CR17","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s11589-998-0035-5","volume":"11","author":"J Liu","year":"1998","unstructured":"Liu, J., Vere-Jones, D., Ma, L., Shi, Y.-L., Zhuang, J.-C.: The principle of coupled stress release model and its application. Acta Seismologica Sinica 11(3), 273\u2013281 (1998)","journal-title":"Acta Seismologica Sinica"},{"issue":"2","key":"9845_CR18","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1093\/biomet\/65.2.297","volume":"65","author":"GM Ljung","year":"1978","unstructured":"Ljung, G.M., Box, G.E.: On a measure of lack of fit in time series models. Biometrika 65(2), 297\u2013303 (1978)","journal-title":"Biometrika"},{"issue":"9","key":"9845_CR19","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1186\/BF03351562","volume":"51","author":"C Lu","year":"1999","unstructured":"Lu, C., Harte, D., Bebbington, M.: A linked stress release model for historical Japanese earthquakes: coupling among major seismic regions. Earth Planets Space 51(9), 907\u2013916 (1999)","journal-title":"Earth Planets Space"},{"key":"9845_CR20","doi-asserted-by":"publisher","first-page":"1838","DOI":"10.1785\/0120130300","volume":"104","author":"W Marzocchi","year":"2014","unstructured":"Marzocchi, W., Taroni, M.: Some thoughts on declustering in probabilistic seismic-hazard analysis. Bull. Seismol. Soc. Am. 104, 1838\u20131845 (2014)","journal-title":"Bull. Seismol. Soc. Am."},{"issue":"6","key":"9845_CR21","doi-asserted-by":"publisher","first-page":"2233","DOI":"10.1785\/0120010267","volume":"92","author":"MV Matthews","year":"2002","unstructured":"Matthews, M.V., Ellsworth, W.L., Reasenberg, P.A.: A Brownian model for recurrent earthquakes. Bull. Seismol. Soc. Am. 92(6), 2233\u20132250 (2002)","journal-title":"Bull. Seismol. Soc. Am."},{"issue":"1","key":"9845_CR22","doi-asserted-by":"publisher","first-page":"69","DOI":"10.2307\/3212408","volume":"12","author":"D Oakes","year":"1975","unstructured":"Oakes, D.: The Markovian self-exciting process. J. Appl. Probab. 12(1), 69\u201377 (1975)","journal-title":"J. Appl. Probab."},{"issue":"401","key":"9845_CR23","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1080\/01621459.1988.10478560","volume":"83","author":"Y Ogata","year":"1988","unstructured":"Ogata, Y.: Statistical models for earthquake occurrences and residual analysis for point processes. J. Am. Stat. Assoc. 83(401), 9\u201327 (1988)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"9845_CR24","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1023\/A:1003403601725","volume":"50","author":"Y Ogata","year":"1998","unstructured":"Ogata, Y.: Space-time point-process models for earthquake occurrences. Ann. Inst. Stat. Math. 50(2), 379\u2013402 (1998)","journal-title":"Ann. Inst. Stat. Math."},{"issue":"3","key":"9845_CR25","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1193\/052015EQS075M","volume":"32","author":"M Ordaz","year":"2016","unstructured":"Ordaz, M., Arroyo, D.: On uncertainties in probabilistic seismic hazard analysis. Earthq. Spectra 32(3), 1405\u20131418 (2016)","journal-title":"Earthq. Spectra"},{"issue":"3","key":"9845_CR26","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1007\/s11009-011-9272-5","volume":"15","author":"JG Rasmussen","year":"2013","unstructured":"Rasmussen, J.G.: Bayesian inference for Hawkes processes. Methodol. Comput. Appl. Probab. 15(3), 623\u2013642 (2013)","journal-title":"Methodol. Comput. Appl. Probab."},{"key":"9845_CR27","volume-title":"The Mechanics of the Earthquake","author":"HF Reid","year":"1910","unstructured":"Reid, H.F.: The Mechanics of the Earthquake, vol. 2. Carnegie Institution of Washington, Washington (1910)"},{"key":"9845_CR28","unstructured":"Ross, G.: Bayesian estimation of the ETAS model for earthquake occurrences. Preprint (2018a)"},{"key":"9845_CR29","unstructured":"Ross, G.: Nonparametric bayesian inference for the Hawkes process with seasonal event data. Preprint (2018b)"},{"issue":"1","key":"9845_CR30","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.tecto.2006.03.005","volume":"423","author":"R Rotondi","year":"2006","unstructured":"Rotondi, R., Varini, E.: Bayesian analysis of marked stress release models for time-dependent hazard assessment in the western Gulf of Corinth. Tectonophysics 423(1), 107\u2013113 (2006)","journal-title":"Tectonophysics"},{"issue":"1","key":"9845_CR31","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1111\/j.1365-246X.2006.03314.x","volume":"169","author":"R Rotondi","year":"2007","unstructured":"Rotondi, R., Varini, E.: Bayesian inference of stress release models applied to some Italian seismogenic zones. Geophys. J. Int. 169(1), 301\u2013314 (2007)","journal-title":"Geophys. J. Int."},{"issue":"2","key":"9845_CR32","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz, G., et al.: Estimating the dimension of a model. Ann. Stat. 6(2), 461\u2013464 (1978)","journal-title":"Ann. Stat."},{"issue":"3","key":"9845_CR33","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1111\/rssb.12062","volume":"76","author":"DJ Spiegelhalter","year":"2014","unstructured":"Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Linde, A.: The deviance information criterion: 12 years on. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 76(3), 485\u2013493 (2014)","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"key":"9845_CR34","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1111\/j.2517-6161.1970.tb00821.x","volume":"32","author":"MA Stephens","year":"1970","unstructured":"Stephens, M.A.: Use of the Kolmogorov-Smirnov, Cram\u00e9r-Von Mises and related statistics without extensive tables. J. R. Stat. Soc. Ser. B (Methodol.) 32, 115\u2013122 (1970)","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"issue":"8","key":"9845_CR35","doi-asserted-by":"publisher","first-page":"3259","DOI":"10.1007\/s12517-013-0930-5","volume":"7","author":"N Tahernia","year":"2014","unstructured":"Tahernia, N., Khodabin, M., Mirzaei, N.: Non-Poisson probabilistic seismic hazard assessment. Arab. J. Geosci. 7(8), 3259\u20133269 (2014)","journal-title":"Arab. J. Geosci."},{"issue":"3","key":"9845_CR36","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1007\/s10651-014-0307-2","volume":"22","author":"E Varini","year":"2015","unstructured":"Varini, E., Rotondi, R.: Probability distribution of the waiting time in the stress release model: the Gompertz distribution. Environ. Ecol. Stat. 22(3), 493\u2013511 (2015)","journal-title":"Environ. Ecol. Stat."},{"issue":"482","key":"9845_CR37","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1198\/016214508000000148","volume":"103","author":"A Veen","year":"2008","unstructured":"Veen, A., Schoenberg, F.P.: Estimation of space-time branching process models in seismology using an em-type algorithm. J. Am. Stat. Assoc. 103(482), 614\u2013624 (2008)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"9845_CR38","doi-asserted-by":"publisher","first-page":"129","DOI":"10.4294\/jpe1952.26.129","volume":"26","author":"D Vere-Jones","year":"1978","unstructured":"Vere-Jones, D.: Earthquake prediction-a statistician\u2019s view. J. Phys. Earth 26(2), 129\u2013146 (1978)","journal-title":"J. Phys. Earth"},{"issue":"3","key":"9845_CR39","doi-asserted-by":"publisher","first-page":"269","DOI":"10.3319\/TAO.2011.12.20.01(T)","volume":"23","author":"J-H Wang","year":"2012","unstructured":"Wang, J.-H., Chen, K.-C., Lee, S.-J., Huang, W.-G., Wu, Y.-H., Leu, P.-L.: The frequency distribution of inter-event times of $$m \\ge 3$$ m \u2265 3 earthquakes in the Taipei metropolitan area: 1973\u20132010. Terr. Atmos. Ocean. Sci. 23(3), 269\u2013281 (2012)","journal-title":"Terr. Atmos. Ocean. Sci."},{"key":"9845_CR40","unstructured":"Wheatley, S.: Extending the Hawkes Process, A General Outlier Test, Case Studies in Extreme Risk. Ph.D. Thesis, ETH Zurich, Zurich (2016)"},{"key":"9845_CR41","unstructured":"Wheatley, S.: Personal communication (2017)"},{"key":"9845_CR42","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.csda.2015.08.007","volume":"94","author":"S Wheatley","year":"2016","unstructured":"Wheatley, S., Filimonov, V., Sornette, D.: The Hawkes process with renewal immigration and its estimation with an EM algorithm. Comput. Stat. Data Anal. 94, 120\u2013135 (2016)","journal-title":"Comput. Stat. Data Anal."},{"issue":"1\u20132","key":"9845_CR43","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0040-1951(94)90007-8","volume":"229","author":"Z Xiaogu","year":"1994","unstructured":"Xiaogu, Z., Vere-Jones, D.: Further applications of the stochastic stress release model to historical earthquake data. Tectonophysics 229(1\u20132), 101\u2013121 (1994)","journal-title":"Tectonophysics"},{"issue":"4","key":"9845_CR44","first-page":"28","volume":"20","author":"W-Z Yang","year":"2000","unstructured":"Yang, W.-Z., Vere-Jones, D., Ma, L., Liu, J.: A method for locating the critical region of a future earthquake using the critical earthquake concept. Earthquake 20(4), 28\u201338 (2000)","journal-title":"Earthquake"},{"issue":"2","key":"9845_CR45","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s11589-002-0006-1","volume":"15","author":"S-B Zhu","year":"2002","unstructured":"Zhu, S.-B., Shi, Y.-L.: Improved stress release model: application to the study of earthquake prediction in Taiwan area. Acta Seismologica Sinica 15(2), 171\u2013178 (2002)","journal-title":"Acta Seismologica Sinica"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-018-9845-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-018-9845-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-018-9845-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T08:31:54Z","timestamp":1720859514000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-018-9845-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,13]]},"references-count":45,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["9845"],"URL":"https:\/\/doi.org\/10.1007\/s11222-018-9845-z","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2018,12,13]]},"assertion":[{"value":"12 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 November 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}