Gambling score in earthquake prediction analysis

Abstract

The number of successes and the space-time alarm rate are commonly used to characterize the strength of an earthquake prediction method and the significance of prediction results. It has been recently suggested to use a new characteristic to evaluate the forecaster's skill, the gambling score (GS), which incorporates the difficulty of guessing each target event by using different weights for different alarms. We expand parametrization of the GS and use the M8 prediction algorithm to illustrate difficulties of the new approach in the analysis of the prediction significance. We show that the level of significance strongly depends (1) on the choice of alarm weights, (2) on the partitioning of the entire alarm volume into component parts and (3) on the accuracy of the spatial rate measure of target events. These tools are at the disposal of the researcher and can affect the significance estimate. Formally, all reasonable GSs discussed here corroborate that the M8 method is non-trivial in the prediction of 8.0 ≤M < 8.5 events because the point estimates of the significance are in the range 0.5-5 per cent. However, the conservative estimate 3.7 per cent based on the number of successes seems preferable owing to two circumstances: (1) it is based on relative values of the spatial rate and hence is more stable and (2) the statistic of successes enables us to construct analytically an upper estimate of the significance taking into account the uncertainty of the spatial rate measure. © 2011 The Authors Geophysical Journal International © 2011 RAS.