Bayesian ETAS: Toward Improved Earthquake Rate Models in the Pacific Northwest

• Activity Number: 413 - Analyses of Environmental Data
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Max Schneider* and Peter Guttorp
• Companies: University of Washington and University of Washington and Norwegian Computing Center
• Keywords: spatiotemporal point process; Bayesian; earthquake; uncertainty quantification; statistical seismology; Epidemic Type Aftershock Sequence

Abstract

The Pacific Northwest (PNW) has substantial earthquake risk and stable models of its earthquake rates are key to probabilistic seismic forecasting for the continental PNW. The Epidemic-Type Aftershock Sequence model (ETAS) is a spatiotemporal point process model which parameterizes the rates of background earthquakes and aftershocks within a seismic region, using a catalog of its past earthquakes. Typically, maximum likelihood estimation is used to fit ETAS to an earthquake catalog; however, the ETAS likelihood suffers from flatness near its optima, parameter correlation and numerical instability, making MLEs less reliable. We present a Bayesian procedure to estimate ETAS parameters, such that parameters can be reliably estimated and their uncertainties resolved. The procedure is conditional on knowing which earthquakes triggered which aftershocks; this latent structure and the ETAS parameters are estimated stepwise, similar to the E-M algorithm. Our procedure uses a Gibbs sampler to conditionally estimate the posterior distributions of model parameters. More detailed information about PNW aftershocks can be estimated using Bayesian ETAS than using simpler seismicity models.