How robust is the skill score of probabilistic earthquake forecasts?

Earthquake scientists continue to improve models of the spatio–temporal evolution of seismicity, including complex aftershock sequences. The Collaboratory for the Study of Earthquake Predictability (CSEP) prospectively evaluates the predictive skill of probabilistic forecasts by such models. Here, we assess the robustness of one popular skill score, the information gain per earthquake, with respect to temporal fluctuations of the seismicity rate. We conduct a numerical experiment with a widely-used temporal stochastic seismicity model, a special case of Hawkes process. Our simulations reveal that the information gain fluctuates substantially with time, because a central limit theorem does not hold in a realistic parameter regime. Our results may eventually contribute to more robust inferences.