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Mathematical Geology

, Volume 33, Issue 1, pp 95–102 | Cite as

An Empirical Bayes Analysis of Volcanic Eruptions

  • Andrew R. Solow
Article

Abstract

This paper describes a simple empirical Bayes approach to inference about the eruption rate of a volcano under a Poisson process model. Under this approach, the prior distribution of the eruption rate is estimated from the eruption records of a group of similar volcanoes. The approach is illustrated using the eruption records of six Central American volcanoes.

bootstrap gamma distribution negative binomial distribution Poisson process 

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REFERENCES

  1. Brillinger, D. R., 1976, Estimation of the second-order intensities of a bivariate stationary point process: Jour. Roy. Stat. Soc., v. B38, no. 1, p. 60–66.Google Scholar
  2. Carlin, B. P., and Louis, T. A., 1996, Bayes and empirical Bayes methods for data analysis: Chapman & Hall, London, 399 p.Google Scholar
  3. Cox, D. R., and Lewis, P. A. W., 1978, The statistical analysis of series of events: Chapman & Hall, London, 285 p.Google Scholar
  4. Deely, J. J., and Lindley, D. V., 1981, Bayes empirical Bayes: Jour. Amer. Stat. Assoc., v. 76, no. 3, p. 833–841.Google Scholar
  5. Gaver, D. P., and O'Muircheartaigh, I. G., 1987, Robust empirical Bayes analyses of event rates: Technometrics, v. 29, no. 1, p. 1–15.Google Scholar
  6. Ho, C., 1990, Bayesian analysis of volcanic eruptions: Jour. Volcanol. Geotherm. Res., v. 43, no. 1.p. 91–98.Google Scholar
  7. Klein, F. W., 1982, Patterns of historical eruptions at Hawaiian volcanoes: Jour. Volcanol. Geotherm. Res., v. 12, no. 1, p. 1–35.Google Scholar
  8. Laird, N. M., and Louis, T. A., 1987, Empirical Bayes confidence intervals based on bootstrap samples: Jour. Amer. Stat. Assoc., v. 82, no. 3, p. 739–757.Google Scholar
  9. Mulgaria, F., Tinti, S., and Boschi, E., 1985, A statistical analysis of flank eruptions on Etna volcano: Jour. Volcanol. Geotherm. Res., v. 23, no. 2, p. 263–272.Google Scholar
  10. Simkin, T., Siebert, L., McClelland, L., Bridge, D., Newhall, C., and Latter, J. H., 1981, Volcanoes of the world: Hutchinson Ross: Stroudsburg, PA, 232 p.Google Scholar
  11. Wickman, F. E., 1976, Markov models of repose-period patterns of volcanoes, in Merriam, D. F., ed., Random processes in geology: Springer, New York, p. 135–161.Google Scholar

Copyright information

© International Association for Mathematical Geology 2001

Authors and Affiliations

  • Andrew R. Solow
    • 1
  1. 1.Woods Hole Ocenographic InstitutionWoods HoleUSA

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