Neural Negative Binomial Regression for Weekly Seismicity Forecasting: Per-Cell Dispersion Estimation and Tail Risk Assessment
It addresses the need for spatially heterogeneous dispersion estimation in earthquake forecasting, enabling better tail risk assessment for seismologists and hazard managers.
This work introduces EarthquakeNet, a neural architecture that estimates per-cell overdispersion for negative binomial regression, improving weekly seismicity forecasting. On Central Asia data (2018-2023), it achieves an 8.6% reduction in MPD and a 12.5% lower CRPS for tail events (Y ≥ 5) compared to a negative binomial GLM baseline.
Standard approaches to forecasting the weekly number of earthquakes on a spatial grid rely on the Poisson distribution with a single global dispersion assumption. We show that this assumption is systematically violated in seismic data from Central Asia (2010-2024), where a likelihood-ratio test with boundary correction strongly rejects the Poisson hypothesis (p < 10^{-179}). The main contribution of this work is the EarthquakeNet architecture, which provides an endogenous per-cell estimate of the overdispersion parameter alpha via a neural network (spatial embeddings + MLP), without explicit spatial covariance specification. In contrast to existing negative binomial regression approaches in seismological forecasting, which typically assume a single global alpha, the proposed per-cell formulation allows the model to identify spatial heterogeneity in seismic clustering and to construct probabilistic risk-aware alerts via quantiles of the predicted distribution. A walk-forward evaluation (2018-2023) over four systems shows an 8.6 percent reduction in mean pinball deviation (MPD) relative to a negative binomial GLM baseline. The strongest improvements are observed in the tail regime (Y >= 5), where the continuous ranked probability score (CRPS) of the proposed model is 12.5 percent lower than that of the baseline, indicating improved calibration in extreme-event forecasting.