Statistical Modelling 10 (2010), 113–132
Extreme value methods for modelling historical series of large volcanic
magnitudes
Claudia Furlan
Dipartimento di Scienze Statistiche
via C. Battisti 241
I–35121 Padova
Italy
eMail: furlan@stat.unipd.it
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.
Keywords:
censored data; change-point model; extreme values; MCMC; volcanic eruptions
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