The Entropy Score and its Uses in Earthquake Forecasting

Abstract

Suppose a forecasting scheme associates a probability p* with some observed outcome. The entropy score given to this forecast is then −logp*. This article provides a review of the background to this scoring method, its main properties, and its relationships to concepts such as likelihood, probability gain, and Molchan’s ν-τ diagram. It is shown that, in terms of this score, an intrinsic characterization can be given for the predictability of a given statistical forecasting model. Uses of the score are illustrated by applications to the stress release and ETAS models, electrical signals, and M8.