Bayesian Estimation of the ETAS Model for Earthquake Occurrences

TL;DR

This paper introduces a scalable Bayesian framework for estimating the ETAS model in earthquake forecasting, explicitly accounting for parameter uncertainty and providing accessible software for large seismic catalogs.

Contribution

A novel scalable Bayesian estimation method for the ETAS model that handles large earthquake catalogs and incorporates parameter uncertainty.

Findings

Efficient Bayesian estimation for large earthquake catalogs.

Explicit representation of parameter uncertainty improves forecast reliability.

Open-source software implementation available.

Abstract

The Epidemic Type Aftershock Sequence (ETAS) model is one of the most widely-used approaches to seismic forecasting. However most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that arises from estimating these from historical earthquake catalogs, resulting in misleadingly optimistic forecasts. In contrast, Bayesian statistics allows parameter uncertainty to be explicitly represented, and fed into the forecast distribution. Despite its growing popularity in seismology, the application of Bayesian statistics to the ETAS model has been limited by the complex nature of the resulting posterior distribution which makes it infeasible to apply on catalogs containing more than a few hundred earthquakes. To combat this, we develop a new framework for estimating the ETAS model in a fully Bayesian manner, which can be efficiently scaled up to large catalogs containing thousands of earthquakes. We also provide easy-to-use software which implements our method.