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Modelling heterogeneous space–time occurrences of earthquakes and its residual analysis

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  • Yosihiko Ogata
  • Koichi Katsura
  • Masaharu Tanemura

Abstract

Summary. Earthquake intensities are modelled as a function of previous activity whose specific form is based on established empirical laws in seismology, but whose parameter values can vary from place to place. This model is used for characterizing regional features of seismic activities in and around Japan, and also for exploring regions where the actual seismicity rate systematically deviates from that of the modelled rate.

Suggested Citation

  • Yosihiko Ogata & Koichi Katsura & Masaharu Tanemura, 2003. "Modelling heterogeneous space–time occurrences of earthquakes and its residual analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 499-509, October.
    • Handle: RePEc:bla:jorssc:v:52:y:2003:i:4:p:499-509
    DOI: 10.1111/1467-9876.00420
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    References listed on IDEAS

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    1. Yosihiko Ogata & Koichi Katsura, 1988. "Likelihood analysis of spatial inhomogeneity for marked point patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 29-39, March.
    2. Yosihiko Ogata & Koichi Katsura & Niels Keiding & Claus Holst & Anders Green, 2000. "Empirical Bayes Age–Period–Cohort Analysis of Retrospective Incidence Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 415-432, September.
    3. F. Musmeci & D. Vere-Jones, 1992. "A space-time clustering model for historical earthquakes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 1-11, March.
    4. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    5. Yosihiko Ogata, 1990. "A Monte Carlo method for an objective Bayesian procedure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 403-433, September.
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    Cited by:

    1. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. A. Baddeley & J. Møller & A. Pakes, 2008. "Properties of residuals for spatial point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 627-649, September.
    3. Frederic Paik Schoenberg & Marc Hoffmann & Ryan J. Harrigan, 2019. "A recursive point process model for infectious diseases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1271-1287, October.
    4. Giada Adelfio & Marcello Chiodi, 2021. "Including covariates in a space-time point process with application to seismicity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 947-971, September.
    5. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    6. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    7. Giada Adelfio & Yosihiko Ogata, 2010. "Hybrid kernel estimates of space–time earthquake occurrence rates using the epidemic-type aftershock sequence model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 127-143, February.
    8. Bent Natvig & Ingunn Fride Tvete, 2007. "Bayesian Hierarchical Space–time Modeling of Earthquake Data," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 89-114, March.

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