Slip-size-dependent renewal processes and Bayesian inferences for uncertainties

Journal of Geophysical Research: Solid Earth

Volumn 107, Issue 11, 2002, Pages

  Ogata, Yosihiko ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Brownian Passage Time process; Lognormal distribution; Posterior distribution; Renewal processes; Time predictable model; Weibull distribution

Indexed keywords

ACTIVE FAULT; BAYESIAN ANALYSIS; EARTHQUAKE RUPTURE; FAULT SLIP; HAZARD ASSESSMENT; SEISMIC HAZARD; UNCERTAINTY ANALYSIS;

EID: 0038556739     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Akaike, H., A new look at the statistical model identification, IEEE Trans. Automat. Control, 19, 716-723, 1974.
2. Akaike, H., A new look at the Bayes procedure, Biometrika, 65, 53-59, 1978.
3. Akaike, H., Likelihood and Bayes procedure, in Bayesian Statistics, edited by J. M. Bernard et al., pp. 1-13, Univ. Press, Valencia, Spain, 1980.
4. Akaike, H., Prediction and entropy, in A Celebration of Statistics. The ISI Centenary Volume, edited by A. C. Atkinson and S. E. Feinberg, pp. 1-24, Springer-Verlag, New York, 1985.
5. Akaike, H., Selected Papers of Horotugu Akaike, edited by E. Parzen, K. Tanabe, and G. Kitagawa, 434 pp., Springer-Verlag, New York, 1998.
6. Box, G. P. B., and G. C. Tiao, Bayesian Inference in Statistical Analysis, 588 pp., Addison-Wesley-Longman, Reading, Mass., 1973.
7. Brillinger, D. R., Seismic risk assessment: Some statistical aspect, Earthquake Predict. Res., 1, 183-195, 1982.
8. Daley, D. J., and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer-Verlag, New York, 1988.
9. Davis, P. M., D. D. Jackson, and Y. Y. Kagan, The longer it has been since the last earthquake, the longer the expected time till the next?. Bull. Seismol. Soc. Am., 79, 1439-1456, 1989.
10. Ellsworth, W. L., M. V. Matthews, R. M. Nadeau, S. P. Nishenko, P. A. Reasenberg, and R. W. Simpson, A physically-based earthquake recurrence model for estimation of long-term earthquake probabilities, paper presented at Second Joint Meeting of the UJNR Panel on Earthquake Research, 1998.
11. Good, I. J, The Estimation of Probabilities, MIT Press, Cambridge, Mass., 1965.
12. Hori, T., and K. Oike, A statistical model of temporal variation of seismicity in the Inner Zone of Southwest Japan related to the interplate earthquakes along the Nankai trough, J. Phys. Earth., 44, 349-356, 1996.
13. Imoto, M., Errors of earthquake probabilities derived from renewal models for recurrent earthquakes (in Japanese), Zisin 11, 52, 337-340, 1999.
14. Matthews, M. V., A stochastic model for recurrent earthquakes, preprint, Walden Consult., Wayland, Mass., 1998.
15. Mulargia, F., and P. Gasperini, Evaluation of the applicability of the time-and slip-predictable earthquake recurrence models to Italian seismicity, Geophys. J. Int., 120, 453-473, 1995.
16. Nakata, T., and K. Shimazaki, Investigation of submarine faults (in Japanese), Kagaku (Science), 63, 593-599, 1993.
17. Nishenko, S. P., and R. Buland, A generic recurrence interval for earthquake forecasting, Bull. Seismol. Soc. Am., 77, 1382-1399, 1987.
18. Ogata, Y., Statistical analysis of uncertain paleoearthquake occurrence times to forecast the hazard of rupture on an active fault segment, J. Geophys. Res., 104, 17,995-18,014, 1999.
19. Ogata, Y., Uncertainties in estimating the hazard of the next Nankai earthquake (in Japanese with English summary and figure captions), Chigaku Zassi (J. Geogr.), 10, 602-614, 2001.
20. O'Hagan, A., Kendall's Advanced Theory of Statistics, vol. 2B, Bayesian Inference, 332 pp., Arnold, London, 1994.
21. Rhoades, D. A., R. J. Van Dissen, and D. J. Dowrik, On the handling of uncertainties in estimating the hazard of rupture on a fault segment, J. Geophys. Res., 99, 13,701-13,712, 1994.
22. Sangawa, A., Seismoarchaeology (in Japanese), 251 pp., Chuokoron-sha, Tokyo, 1992.
23. Savage, J. C., Criticism of some forecasts of the national earthquake prediction evaluation council, Bull. Seismol. Soc. Am., 81, 862-881, 1991.
24. Savage, J. C., The uncertainty in earthquake conditional probabilities, Geophys. Res. Lett., 19, 709-712, 1992.
25. Schrödinger, E., Zur theorie der fall und steigversuche an teilchen mit Brownscher bewegung, Phys. Z., 16, 289-295, 1915.
26. Seshadri, V., The Inverse Gaussian Distribution, Lect. Notes Stat., vol. 137, 347 pp., Springer-Verlag, New York, 1998.
27. Shimazaki, K., and T. Nakata, Time-predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, 279-282, 1980.
28. Usami, T., Materials for Comprehensive List of Destructive Earthquakes in Japan, 416-1995 (in Japanese), 494 pp., Univ. of Tokyo Press, Tokyo, 1996.
29. Utsu, T., Recurrence of several earthquakes at almost equal time intervals (in Japanese), Zisin 11, 47, 93-95, 1994.
30. Utsu, T., Seismicity Studies: A Comprehensive Review, 876 pp., Univ. of Tokyo Press, Tokyo, 1999.
31. Working Group on Assessment Methods of Long Term Earthquake Probability, Report on the assessment methods of long term earthquake probability and some applied examples (in Japanese), 74 pp., Comm. of Earthquake Res., Headquarters for Earthquake Res. Promotion, Prime Minist. Off., Tokyo, 2001.
32. Working Group on California Earthquake Probabilities, Probability of large earthquakes occuring in California on the San Andreas Fault, U. S. Geol. Surv. Open File Rep., 88-398, 1988.
33. Working Group on California Earthquake Probabilities, Seismic hazards in southern California: Probable earthquakes, 1994 to 2024, Bull. Seismol. Soc. Am., 85, 379-439, 1995.