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Mathematical Geosciences

, Volume 43, Issue 5, pp 505–519 | Cite as

On Selection of Analog Volcanoes

  • Armando Rodado
  • Mark Bebbington
  • Alasdair Noble
  • Shane Cronin
  • Gill Jolly
Article

Abstract

Estimating the occurrence probability of volcanic eruptions with VEI ≥3 is challenging in several aspects, including data scarcity. A suggested approach has been to use a simple model, where eruptions are assumed to follow a Poisson process, augmenting the data used to estimate the eruption onset rate with that from several analog volcanoes. In this model the eruption onset rate is a random variable that follows a gamma distribution, the parameters of which are estimated by an empirical Bayes analysis. The selection of analog volcanoes is an important step that needs to be explicitly considered in this model, as we show that the analysis is not always feasible due to the required over-dispersion in the resulting negative binomial distribution for the numbers of eruptions. We propose a modification to the method which allows for both over-dispersed and under-dispersed data, and permits analog volcanoes to be chosen on other grounds than mathematical tractability.

Keywords

Empirical Bayes Conway–Maxwell–Poisson process Information gain 

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Copyright information

© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  • Armando Rodado
    • 1
  • Mark Bebbington
    • 2
  • Alasdair Noble
    • 3
  • Shane Cronin
    • 2
  • Gill Jolly
    • 4
  1. 1.IFS–StatisticsMassey UniversityPalmerston NorthNew Zealand
  2. 2.Volcanic Risk SolutionsMassey UniversityPalmerston NorthNew Zealand
  3. 3.Plant and Food Research LimitedLincolnNew Zealand
  4. 4.GNS ScienceTaupoNew Zealand

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