Credible probabilities for the time occurrence of extreme space-weather events

Statistical analysis is made of rare, extreme space-weather events recorded in historical data -- counting the number of events with sizes that exceed chosen thresholds during specific durations of time. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. For "error bars" the frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate. If only a few events have been observed, as is usually the case for extreme events, then these intervals might be considered to be relatively wide. As examples, 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 magnetic storms.