Magnitude-weighted goodness-of-fit scores for earthquake forecasting

Frederic Schoenberg

Published June 2025, SCEC Contribution #14993

Current methods for evaluating earthquake forecasts, such as the N-test, L-test, or log-likelihood score, typically do not disproportionately reward a model for more accurately forecasting the largest events, or disproportionately punish a model for less accurately forecasting the largest events. However, since the largest earthquakes are by far the most destructive and therefore of most interest to practitioners, in many circumstances, a weighted likelihood score may be more useful. Here, we propose various weighted measures, weighting each earthquake by some function of its magnitude, such as potency-weighted log-likelihood, and consider their properties. The proposed methods are applied to a catalog of earthquakes in the Western United States.

Citation
Schoenberg, F. (2025). Magnitude-weighted goodness-of-fit scores for earthquake forecasting. Spatial Statistics, 67. https://doi.org/10.1016/j.spasta.2025.100895.