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

• Published in: Geophysical research letters 2012-05, Vol.39 (10), p.n/a
• Main Author: Love, Jeffrey J.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Confidence intervals; Earth sciences; Earth, ocean, space; Earthquakes; Exact sciences and technology; extreme events; forecast probability; Forecasting; Geophysics; Inference; Intervals; Magnetic storms; Mathematical models; Mathematics; Probability; Seismic activity; Seismic phenomena; Seismology; Space; Statistical analysis; statistical inference; Volcanic eruptions; Volcanoes; Weather forecasting
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2012GL051431

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 τ.Under transformations that stabilize data and model‐parameter variances, the most likely Poisson‐event occurrence rate,k/τ, 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/τ)(k−z/2)2,(k+z/2)2 , where z is a parameter that specifies the width, z = 1 (z = 2) corresponding to 1σ, 68.3% (2σ, 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. Key Points Extreme‐event occurrence rates and uncertainty intervals are derived Frequentist and Bayesian (Jeffreys) mathematics are approximately the same Extreme‐event probabilities are forecasted