Analysing the interevent time distribution to identify seismicity phases: A Bayesian nonparametric approach to the multiple-changepoint problem

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 49, Issue 4, 2000, Pages 543-562

  Pievatolo, Antonio ^a   Rotondi, Renata ^a  

^a CNR   (Italy)

Author keywords

Bayesian nonparametric inference; Distribution estimation; Generalized gamma distribution; Mixture of Dirichlet processes; Reversible jump Markov chain Monte Carlo methods; Seismicity phase

Indexed keywords

EID: 0034354507     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.00211     Document Type: Article

References (40)

1. Anagnos, T. and Kiremidjian, A. S. (1988) A review of earthquake occurrence models for seismic hazard analysis. Probab. Engng Mech., 3, 3-11.
2. Antoniak, C. E. (1974) Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist., 2, 1152-1174.
3. Barry, D. and Hartigan, J. A. (1993) A Bayesian analysis for changepoint problems. J. Am. Statist. Ass., 88, 309-319.
4. Benioff, H. (1951) Colloquium on plastic flow and deformation within the earth. Trans. Am. Geophys. Un., 32, 508-514.
5. Brodsky, B. E. and Darkhovsky, B. S. (1993) Nonparametric Methods in Changepoint Problems. Dordrecht: Kluwer.
6. Bullen, K. K. and Bolt, B. A. (1985) An Introduction to the Theory of Seismology. Cambridge: Cambridge University Press.
7. Camassi, R. and Stucchi, M. (1997) NT4.1.1 - a Parametric Catalogue of Damaging Earthquakes in the Italian Area. Rome: Gruppo Nazionale per la Difesa dai Terremoti. (Available from http://emidius.itim.mi.cnr.it/ NT/home,html.)
8. Carlin, B. P., Gelfand, A. E. and Smith, A. F. M. (1992) Hierarchical Bayesian analysis of changepoint problems. Appl. Statist., 41, 389-405.
9. Di Filippo, D. and Marcelli, L. (1950) Magnitudo ed energia dei terremoti in Italia. Ann. Geofis., 3, 337-348.
10. Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Ann. Statist., 1, 209-230.
11. Gaetan, C. and Pievatolo, A. (1996) Change-point analysis in stochastic processes. In Statistical Modelling (eds A. Forcina, G. M. Marchetti, R. Hatzinger and G. Galmacci). Città di Castello: Graphos.
12. Gardner, J. K. and Knopoff, L. (1974) Is the sequence of earthquake in Southern California, with aftershocks removed, Poissonian? Bull. Seismol. Soc. Am., 64, 1363-1367.
13. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337-348.
14. Green, P. J. (1995) Reversible jump MCMC computation and Bayesian model determination. Biometrika, 82, 711-732.
15. Gutenberg, B. and Richter, C. F. (1942) Earthquake magnitude, intensity, energy and acceleration. Bull. Seismol. Soc. Am., 32, 163-191.
16. Habermann, R. E. (1982) Seismicity rates in the Kuriles Island Arc, 1963-1979. Earthq. Predn Res., 1, 73-94.
17. _(1987) Man-made changes of seismicity rates. Bull. Seismol. Soc. Am., 77, 141-159.
18. Kashiwagi, N. (1991) Bayesian detection of structural changes. Ann. Inst. Statist. Math., 43, 77-93.
19. Lomnitz, C. (1994) Fundamentals of Earthquake Prediction. New York: Wiley.
20. Matthews, M. V. and Reasenberg, P. A. (1988) Statistical methods for investigating quiescence and other temporal seismicity patterns. Pure Appl. Geophys., 126, 357-372.
21. McCulloch, R. E. and Tsay, R. S. (1993) Bayesian analysis of threshold autoregressive processes with a random number of regimes. In Computing Science and Statistics: Proc. 25th Symp. Interface, pp. 253-262. Fairfax Station: Interface Foundation of North America.
22. Meyn, S. P. and Tweedie, R. L. (1993) Markov Chains and Stochastic Stability. London: Springer.
23. Mira, A. and Petrone, S. (1996) Bayesian hierarchical nonparametric inference for change-point problems. In Bayesian Statistics 5 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 693-703. Oxford: Oxford University Press.
24. Muliere, P. and Scarsini, M. (1985) Change-point problems: a Bayesian nonparametric approach. Apl. Mat., 30, 397-402.
25. _(1993) Some aspects of change-point problems. In Reliability and Decision Making (eds R. E. Barlow, C. A. Clarotti and F. Spizzichino), pp. 273-285. London: Chapman and Hall.
26. Petrone, S. and Raftery, A. (1997) A note on the Dirichlet process prior in Bayesian non-parametric inference with partial exchangeability. Statist. Probab. Lett., 36, 69-83.
27. Raftery, A. E. (1994) Change-point and change curve modelling in stochastic processes and spatial statistics. J. Appl. Statist. Sci., 1, 403-424.
28. Raftery, A. E. and Akman, V. E. (1986) Bayesian analysis of a Poisson process with a change-point. Biometrika, 73, 85-89.
29. s a partire da dati macrosismici per i terremoti compresi nei cataloghi NT. Technical Report. Gruppo Nazionale per la Difesa dai Terremoti, Consiglio Nazionale delle Ricerche, Rome.
30. Rotondi, R. (1999) Statistical analysis of temporal variations of seismicity level in some Italian regions. Nat. Hazards, 19, 139-150.
31. Rotondi, R. and Pagliano, P. (1994) The problem of completeness of a seismic catalog: a change-point problem. In Applications on the Prevention and Forecasting of Earthquakes: Proc. 2nd Wrkshp Statistical Models and Methods, Cephalonia, June 2nd-5th, 1993 (eds G. A. Papadopoulos and K. C. Makropoulos), pp. 170-182.
32. Scandone, P., Patacca, E., Meletti, C., Bellatalla, M., Perilli, N. and Santini, U. (1992) Struttura geologica, evoluzione cinematica e schema sismotettonico della penisola italiana. In Zonazione e Riclassificazione Sismica: Proc. Conf. Gruppo Nazionale per la Difesa dai Terremoti, Pisa, June 25th-27th, 1990, vol. 1, pp. 119-135. Bologna: Ambiente.
33. Sethuraman, J. (1994) A constructive definition of Dirichlet priors. Statist. Sin., 4, 639-650.
34. Sieh, H. K., Stuiver, M. and Brillinger, D. (1989) A more precise chronology of earthquakes produced by the San Andreas fault in Southern California. J. Geophys. Res., 94, 603-623.
35. Smith, A. F. M. (1975) A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika, 62, 407-416.
36. _(1980) Change-point problems: approaches and applications. Trab. Estad. Invest. Oper., 31, 83-98.
37. Stephens, D. A. (1994) Bayesian retrospective multiple change-point identification. Appl. Statist., 43, 159-178.
38. Stephens, D. A. and Smith, A. F. M. (1993) Bayesian edge-detection in images via change-point methods. In Computer Intensive Methods in Statistics (eds W. Härdle and L. Simar), pp. 1-29. Heidelberg: Physica.
39. Tinti, S. and Mulargia, F. (1985) Completeness analysis of a seismic catalog. Ann. Geophys., 3, 407-414.
40. Vere-Jones, D. (1995) Forecasting earthquakes and earthquake risk. Int. J. Forecast., 11, 503-538.