A Bayesian analysis for the seismic data on Taiwan

  • Tsai-Hung Fan
  • Eng-Nan Kuo
Seismic Data Analysis

Abstract

A Bayesian approach is used to analyze the seismic events with magnitudes at least 4.7 on Taiwan. Following the idea proposed by Ogata (1988,Journal of the American Statistical Association,83, 9–27), an epidemic model for the process of occurrence times given the observed magnitude values is considered, incorporated with gamma prior distributions for the parameters in the model, while the hyper-parameters of the prior are essentially determined by the seismic data in an earlier period. Bayesian inference is made on the conditional intensity function via Markov chain Monte Carlo method. The results yield acceptable accuracies in predicting large earthquake events within short time periods.

Key words and phrases

Epidemic model prior distribution hyperparameter conditional intensity function MCMC method 

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References

  1. Akaike, H. (1974). A new look at the statistical model identification,IEEE Transactions on Automatic Control,19, 716–723.MATHMathSciNetCrossRefGoogle Scholar
  2. Berger, J. O. (1985).Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York.MATHGoogle Scholar
  3. Betrò, B. and Ladelli, L. (1996). Point process analysis for Italian seismic activity,Applied Stochastic Models and Data Analysis,12, 75–105.MATHCrossRefGoogle Scholar
  4. Daley, D. and Vere-Jones, D. (1988).An Introduction to the Theory of Point Processes, Springer-Verlag, New York.MATHGoogle Scholar
  5. Fan, T. H. and Lin, J. S. (2002). A Bayesian analysis for the seismic data in Hualien area,Journal of Chinese Statistical Association,40, 229–247.Google Scholar
  6. Musmeci, F. and Vere-Jones, D. (1992). A space-time clustering model for historical earthquakes,Annals of the Institute of Statistical Mathematics,44, 1–11.CrossRefGoogle Scholar
  7. Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes,Journal of the American Statistical Association,83, 9–27.CrossRefGoogle Scholar
  8. Ogata, Y. (1989). Statistical model for standard seismicity and detection of anomalies by residual analysis,Tectonophysics,169, 159–174.CrossRefGoogle Scholar
  9. Ogata, Y. (2002). Slip-size-dependent renewal processes and Bayesian inferences for uncertainties,Journal of Geophysical Research,107 (B11), 2268, doi: 10.1029/2001JB000668.CrossRefGoogle Scholar
  10. Ogata, Y. and Katsura, K. (1988). Likelihood analysis of spatial inhomogeneity for marked point patterns,Annals of the Institute of Statistical Mathematics,40, 29–39.MATHMathSciNetCrossRefGoogle Scholar
  11. Peruggia, M. and Santner, T. (1996). Bayesian analysis of time evolution of earthquakes,Journal of the American Statistical Association,91, 1209–1218.MATHCrossRefGoogle Scholar
  12. Rhoades, D. A., Van Dissen, R. J. and Dowrik, D. J. (1994). On the handling of uncertainties in estimating the hazard of rupture on a fault segment,Journal of Geophysical Research,99, 13701–13712.CrossRefGoogle Scholar
  13. Schwarz, G. (1978). Estimating the dimension of a model,The Annals of Statistics,6, 461–464.MATHMathSciNetGoogle Scholar
  14. Utsu, T. (1961). A statistical study on the occurrence of aftershocks,Geophysical Magazine,30, 521–605.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 2004

Authors and Affiliations

  • Tsai-Hung Fan
    • 1
  • Eng-Nan Kuo
    • 1
  1. 1.Graduate Institute of StatisticsNational Central UniversityChungliTaiwan R.O.C.

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