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

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) [(root k - z/2)(2), (root 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: Love, J. J. (2012), Credible occurrence probabilities for extreme geophysical events: Earthquakes, volcanic eruptions, magnetic storms, Geophys. Res. Lett., 39, L10301, doi:10.1029/2012GL051431.