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.
Suggested Citation
Love, J.J., 2012, Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms: Geophysical Research Letters, v. 39, no. 10, L10301, https://doi.org/10.1029/2012GL051431.
| 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 |
| Publication Date | May 18, 2012 |
| 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 |