Decision theory and the analysis of rare event space weather forecasts

[1] Several basic results from decision theory as applied to rare event forecasts are reviewed, and an alternative method for comparing rare event forecasts is presented. A fundamental result is that for a large class of users only interested in economic utility, the relevant performance quantity is the number of correct and false alarm forecasts. This is contrasted with the reality that most forecast models are optimized to have a high data-model correlation, which does not always correspond to maximum economic utility. The value score ( VS) developed by Wilks ( 2001) partially resolves this disconnect between modeler- and user-relevant metrics. Although the value score is closer to what is most likely of interest to a user, maximal VS does not necessarily correspond to maximal utility for the realistic case where the cost and benefit are dependent on the amplitude of the forecasted event. An alternative comparison and presentation method is proposed which may resolve this problem. For the class of users considered, full specification of model performance requires computation of the probability of correct, false alarm, and missed forecasts at several amplitude levels and warning time spans. Examples of the computations involved for the modeler and user are given for predictions of large-amplitude energetic electron fluence and geomagnetic storms parameterized by the Dst index.