Fitting the background intensity in ETAS models using regression-based poisson point process models

The Epidemic-Type Aftershock Sequence model (ETAS) is a widely used self-exciting spatio-temporal point process for earthquake occurrence, in which seismicity is represented as the superposition of background events and triggered events. In many ETAS implementations, the background component is estimated non-parametrically, typically through kernel smoothing. Although flexible, this approach can limit formal inference and make it difficult to incorporate structured information, such as spatial covariates and mark-related features, into the background component. This paper proposes an ETAS formulation with a regression-based background component. The standard ETAS triggering structure and declustering logic are preserved, while the background component is modelled using a regression-based approach. This provides a more interpretable representation of background seismicity and extends the range of information that can be incorporated into ETAS models. We evaluate the proposed methodology through a simulation study and illustrate its practical usefulness with an application to an Italian earthquake catalogue. The results show that the proposed approach improves the recovery of structured background intensities while maintaining competitive estimation of the triggered component.