Neural Negative Binomial Regression for Weekly Seismicity Forecasting: Per-Cell Dispersion Estimation and Tail Risk Assessment

TL;DR

This paper introduces EarthquakeNet, a neural network architecture that estimates per-cell dispersion in seismic data, improving weekly earthquake forecasts and tail risk assessment over traditional Poisson models.

Contribution

EarthquakeNet provides endogenous per-cell overdispersion estimates using neural networks, capturing spatial heterogeneity and enhancing probabilistic seismic risk forecasting.

Findings

8.6% reduction in mean pinball deviation compared to baseline

12.5% lower CRPS in tail regime, indicating better extreme-event calibration

Likelihood-ratio test strongly rejects Poisson hypothesis in seismic data

Abstract

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.