Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

TL;DR

This paper introduces a Bayesian approach to modeling earthquake occurrences using a semiparametric Hawkes process, allowing for uncertainty quantification in spatial earthquake predictions.

Contribution

It develops a fully Bayesian ETAS model with a nonparametric prior for the mainshock distribution, improving over traditional point estimate methods.

Findings

Enhanced uncertainty quantification in earthquake modeling

Efficient inference via auxiliary latent variables

Improved flexibility in spatial earthquake prediction

Abstract

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.