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

Geophysical Research Letters

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DOI: 10.1029/2012GL051431

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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