Bayesian Inference for Solar Flare Extremes

While solar flares are a frequent occurrence, extreme flares are much rarer events and have the potential to cause disruption to life on Earth. In this paper we use Extreme Value Theory to model extreme solar flares, with inference performed in the Bayesian paradigm. The data used have been provided by the National Oceanic and Atmospheric Organisation and consist of recordings of peak flux measurements. After proposing several methods for analysis and selecting our preferred technique—which substantially increases the precision of estimates of key quantities of interest—we improve upon this technique still further by considering the use of informative prior distributions. Doing so, we estimate that a Halloween‐type solar event , and a Carrington‐type event , might occur once (on average) every 49 (29, 85) and 92 (50, 176) years respectively (95% credible intervals shown in parentheses). These findings are similar to those obtained by Tsiftsi and De la Luz (2018), https://doi.org/10.1029/2018SW001958 and Elvidge and Angling (2018), https://doi.org/10.1002/2017SW001727 however, the confidence intervals obtained in both are substantially wider than those found in our study, lending increased certainty to the estimated time between events of such magnitude in our work. We argue that taking the extremal index into account, even when this measure indicates weak temporal dependence, is beneficial to the analysis.