Gambling scores for earthquake predictions and forecasts

SUMMARY

This paper presents a new method, namely the gambling score, for scoring the performance earthquake forecasts or predictions. Unlike most other scoring procedures that require a regular scheme of forecast and treat each earthquake equally, regardless their magnitude, this new scoring method compensates the risk that the forecaster has taken. Starting with a certain number of reputation points, once a forecaster makes a prediction or forecast, he is assumed to have betted some points of his reputation. The reference model, which plays the role of the house, determines how many reputation points the forecaster can gain if he succeeds, according to a fair rule, and also takes away the reputation points betted by the forecaster if he loses. This method is also extended to the continuous case of point process models, where the reputation points betted by the forecaster become a continuous mass on the space–time–magnitude range of interest. We also calculate the upper bound of the gambling score when the true model is a renewal process, the stress release model or the ETAS model and when the reference model is the Poisson model.