Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T17:53:01.256Z Has data issue: false hasContentIssue false
  • English
  • Français

Point-process models with linearly parametrized intensity for application to earthquake data

Published online by Cambridge University Press:  14 July 2016

Yosihiko Ogata  and
Koichi Katsura
Get access Rights & Permissions [Opens in a new window]

Abstract

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set.

Some technical aspects of the modelling and calculations are described.

Keywords

CONDITIONAL INTENSITY FUNCTIONMAXIMUM LIKELIHOOD ESTIMATESTRENDCYCLIC AND CLUSTERING DECOMPOSITIONCAUSAL RELATION OF SHOCK SEQUENCESRESPONSE FUNCTIONSAKAIKE INFORMATION CRITERIONEARTHQUAKE MIGRATION
Type
Part 5—Random Fields and Point Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 291 - 310
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1977) On entropy maximization principle. In Application of Statistics ed. Krishnaiah, P. R., North-Holland, Amsterdam, 27–41.Google Scholar
Akaike, H. (1983) Information measure and model selection. Proc. 44th Session Internat. Statistical Inst.,Madrid, Spain, September 12-22, 1983. Bull. Internat. Statist. Inst. 50(1), 277–291.Google Scholar
Fletcher, R. and Powell, M. J. D. (1963) A rapidly convergent descent method for minimization. Computer J. 6, 163–168.Google Scholar
Hawkes, A. G. and Adamopoulos, L. (1973) Cluster models for earthquakes–regional comparison. Bull. Internat. Statist. Inst. 45, 454–461.Google Scholar
Lewis, P. A. W. and Shedler, G. S. (1979) Simulation of non-homogeneous Poisson processes by thinning. Naval Res. Logist. Quart. 26, 403–413.CrossRefGoogle Scholar
Liptzer, R. S. and Shiryaev, A. N. (1978) Statistics of Random Processes II, Applications. Springer-Verlag, New York.Google Scholar
Mogi, K. (1973) Relationship between deep and shallow seismicity in the Western Pacific region. Tectonophysics 17, 1–22.CrossRefGoogle Scholar
Muirhead, K. J. (1981) Seismicity induced by the filling of the Talbingo Reservoir. J. Geol. Soc. Austral. 28, 291–298.Google Scholar
Ogata, Y. (1981) On Lewis' simulation method for point processes. IEEE Trans. Inform. Theory IT-27, 23–31.CrossRefGoogle Scholar
Ogata, Y. (1983) Likelihood analysis of point process and its application to seismological data. Proc. 44th Session Internat. Statistical Inst., Madrid, Spain, September 12-22, 1983. Bull. Internat. Statist. Inst. 50(2), 943–961.Google Scholar
Ogata, Y. and Akaike, H. (1982a) On linear intensity models for mixed doubly stochastic Poisson and self-exciting point processes. J. R. Statist. Soc. B 44, 102–107.Google Scholar
Ogata, Y., Akaike, H. and Katsura, K. (1982b) The application of linear intensity models to the investigation of causal relations between a point process and another stochastic process. Ann. Inst. Statist. Math. B 34, 373–387.Google Scholar
Utsu, T. (1975) Correlation between shallow earthquakes in Kwanto region and intermediate earthquakes in Hida region, central Japan. Zisin (J. Seism. Soc., Japan) 2nd Ser. 28, 303–311 (in Japanese).Google Scholar
Vere-Jones, D. (1970) Stochastic models for earthquake occurrence (with discussion). J. R. Statist. Soc. B 32, 1–62.Google Scholar
Vere-Jones, D. and Ozaki, T. (1982) Some examples of statistical inference applied to earthquake data. Ann. Inst. Stat. Math. 34, 189–207.CrossRefGoogle Scholar