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

TL;DR

This paper introduces GP-ETAS, a Bayesian semiparametric model for earthquake aftershock sequences that uses Gaussian processes to better estimate spatial background intensity and quantify uncertainty.

Contribution

It proposes a novel Bayesian GP-ETAS model with efficient Gibbs sampling for improved inference and uncertainty quantification in earthquake modeling.

Findings

GP-ETAS outperforms standard models on synthetic data

Provides accurate uncertainty quantification

Demonstrates effectiveness on real earthquake data

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.