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

April 22, 2013

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.

Citation Information

Publication Year 2012
Title Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms
DOI 10.1029/2012GL051431
Authors Jeffrey J. Love
Publication Type Article
Publication Subtype Journal Article
Series Title Geophysical Research Letters
Series Number
Index ID 70045154
Record Source USGS Publications Warehouse
USGS Organization Geologic Hazards Science Center

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