The Q-Score: A Magnitude-Weighted Goodness-of-Fit Score for Earthquake Forecasting

Alejandra Arjon, Julia Jansson Valter, Francesco Serafini, & Frederic Schoenberg

Submitted August 30, 2026, SCEC Contribution #15336, 2026 SCEC Annual Meeting Poster #205

Earthquake occurrences are often modelled with spatial-temporal point process models, such as the Epidemic-Type-Aftershock-Sequence (ETAS) model. Comparing models and assessing goodness-of-fit of earthquake forecasts can be done using tests developed by the Collaboratory for the Study of Earthquake Predictability (CSEP). However, most current earthquake forecast evaluation metrics, such as the N-test and L-test, do not give additional weight to large magnitude events. To this end, magnitude weighted goodness-of-fit scores for earthquake forecasting have recently been introduced, such as potency weighted log-likelihood and the Q-score. We define and further investigate the Q-score, which is a quotient emphasizing model fit for the 5% largest earthquakes. Under certain regularity conditions, the expectation of the Q-score should be close to 1, and it satisfies a law of large numbers. The Q-score is evaluated for 21 CSEP next-day gridded forecasts for California earthquake data from 2012, 2014, and 2017. We also compare the log-likelihood scores of the forecasts to assess how well different models, such as ETAS, perform, both for predicting the largest events but also in terms of overall model fit.

Citation
Arjon, A., Jansson Valter, J., Serafini, F., & Schoenberg, F. (2026, 08). The Q-Score: A Magnitude-Weighted Goodness-of-Fit Score for Earthquake Forecasting. Poster Presentation at 2026 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)