Extreme value methods for modelling historical series of large volcanic magnitudes

Abstract

Volcanic eruptions are among the most extreme events on earth and it seems natural to make use of the theory of extreme values to improve understanding of volcanic pocesses. The dataset we use is a catalogue of large eruptions over the last two millennia, in which the date of occurrence and magnitude are recorded. The dataset is affected by a recording bias, mostly for eruptions of lower magnitude, though this under-recording process largely disappears in the most recent 400 years. Coles and Sparks modelled these data, via maximum likelihood, using a Poisson process motivated by extreme value theory, with an intensity function that takes into account the recording bias. Nevertheless, the fitted model did not seem entirely consistent with the observed data, since this intensity function does not represent effectively the temporal evolution of the censoring effect in the recording process. The aim of the paper is to provide a more flexible model that might fit better the under-recording process, through an alternative intensity function based on a change-point model. Moreover, the Bayesian context we use allows us to refine some inferential aspects of the return period calculation to improve forecast accuracy.