A Likelihood‐Free Framework for Seismic Forecasting Models: Application to Incomplete ETAS Model via Simulation‐Based Inference

Abstract

Recent advances in deep‐learning‐based earthquake detection have revolutionized seismology, producing high‐resolution catalogs complete down to very low magnitudes. While these data sets offer an unprecedented view of seismic triggering, their massive scale and inherent short‐term incompleteness pose a major challenge for traditional statistical analysis. In this context, identifying the optimal model parameters for forecasting becomes challenging. Indeed, the standard procedure of maximizing the likelihood is often unfeasible, due to both the massive volume of data and the fact that observations are strongly biased by incompleteness. To address this, here we reformulate parameter estimation as a likelihood‐free, simulation‐based inverse problem. We introduce a general framework that bypasses the explicit evaluation of the likelihood by combining Approximate Bayesian Computation with stochastic optimization. The method performs inference by identifying the parameter set that minimizes the discrepancy between the observed data and a stochastic generative model, using summary statistics that capture the essential spatio‐temporal features of the triggering process. We validate this approach using the incomplete Epidemic‐Type Aftershock Sequence (ETAS) model, which explicitly incorporates time‐dependent detection thresholds. Tests on synthetic catalogs demonstrate that the framework robustly recovers the underlying physical parameters even under severe incompleteness, revealing systematic biases in standard ETAS estimates that ignore detection limitations. Notably, the proposed method exhibits sub‐quadratic computational scaling with catalog size, enabling the analysis of the vast data sets produced by modern monitoring networks. Our approach provides a scalable and flexible solution for the next generation of seismic forecasting.