GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model

Abstract

The spatio-temporal Epidemic Type Aftershock Sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a full Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.

A systematic approach and software for the analysis of point patterns on river networks

“…Hawkes processes (Hawkes, 1971) are self-exciting processes, that is the occurrence of an event can trigger a sequence of future events. This class of point processes has been widely used to model spatio-temporal seismicity patterns (mainshocks and aftershocks) (Ogata, 1998;Molkenthin et al, 2020).…”

Is Seismicity Operating at a Critical Point?

“…In some other studies, such as [40], the spatial probability density function (PDF) of background earthquakes is pre-estimated and then fed into the ETAS inversion machinery. Furthermore, [41,29,42] infer the optimal space variation of all ETAS parameters jointly, while more recently, [43] have proposed an alternative approach to non-parametrically model the space variation of background rate using a Gaussian process prior.…”