Extreme value methods for modelling historical series of large volcanic magnitudes
Published:January 01, 2006
S. G. Coles, R. S. J. Sparks, 2006. "Extreme value methods for modelling historical series of large volcanic magnitudes", Statistics in Volcanology, H. M. Mader, S. G. Coles, C. B. Connor, L. J. Connor
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Extreme value theory sits alone in the statistical sciences. It is the branch of statistics devoted to the inference of extreme events in random processes, and differs from most areas of statistics in modelling rare, rather than typical, behaviour. A common aim is to estimate what future extreme levels of a process might be expected based on a historical series of observations. As such, the methodology is widely used in engineering applications that need an assessment of extreme environmental conditions: for example, sea levels, wind speeds or river flow (Coles 2001, chapter 1). Another recent area of application is to financial markets, for which calculations on the plausibility of large returns (postitive or negative) are helpful, and even a statutory requirement for many banks (e.g. Embrechts et al. 1998).
Volcanic events are among the most explosive on Earth. A recent study (Mason et al. 2004) has compared the potential damage from large volcanoes with that of other potentially catastrophic events, such as a meteor strike. At least in an informal sense therefore, they are extreme events, and it seems reasonable to hope that extreme value theory can make a useful contribution to their analysis. In this paper we explore this possibility. We take the recent history of large eruptive volcanoes, and apply extreme value techniques to obtain estimates of the probability of future extreme eruption events at different levels of magnitude. Such inferences are of general volcanologi-cal interest, but they are also directly .
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Statistics in Volcanology
Statistics in Volcanology is a comprehensive guide to modern statistical methods applied in volcanology written by today's leading authorities. The volume aims to show how the statistical analysis of complex volcanological data sets, including time series, and numerical models of volcanic processes can improve our ability to forecast volcanic eruptions. Specific topics include the use of expert elicitation and Bayesian methods in eruption forecasting, statistical models of temporal and spatial patterns of volcanic activity, analysis of time series in volcano seismology, probabilistic hazard assessment, and assessment of numerical models using robust statistical methods. Also provided are comprehensive overviews of volcanic phenomena, and a full glossary of both volcanological and statistical terms.
Statistics in Volcanology is essential reading for advanced undergraduates, graduate students, and research scientists interested in this multidisciplinary field.