Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms

Geophysical Research Letters
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Abstract

Statistical analysis is made of rare, extreme geophysical events recorded in historical data -- counting the number of events $k$ with sizes that exceed chosen thresholds during specific durations of time $\tau$. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate, $k/\tau$, applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. Frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate: $(1/\tau)[(\sqrt{k} - z/2)^{2},(\sqrt{k} + z/2)^{2}]$, where $z$ is a parameter that specifies the width, $z=1$ ($z=2$) corresponding to $1\sigma$, $68.3\%$ ($2\sigma$, $95.4\%$). If only a few events have been observed, as is usually the case for extreme events, then these "error-bar" intervals might be considered to be relatively wide. From historical records, we estimate most likely long-term occurrence rates, 10-yr occurrence probabilities, and intervals of frequentist confidence and Bayesian credibility for large earthquakes, explosive volcanic eruptions, and magnetic storms.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms
Series title Geophysical Research Letters
DOI 10.1029/2012GL051431
Volume 39
Issue 10
Year Published 2012
Language English
Publisher AGU
Publisher location Washington, D.C.
Contributing office(s) Geologic Hazards Science Center
Description L10301
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Geophysical Research Letters