Mathematical Geology

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

An Empirical Bayes Analysis of Volcanic Eruptions

  • Andrew R. Solow


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations