SCEC Award Number 09150 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Parameter Estimation for Earthquake Clustering Models
Investigator(s)
Name Organization
David Jackson University of California, Los Angeles
Other Participants Wang, Qi
SCEC Priorities A10, A4 SCEC Groups Seismology, EFP, WGCEP
Report Due Date 02/28/2010 Date Report Submitted N/A
Project Abstract
 The epidemic-type aftershock sequence (ETAS) model is a self-exciting point process model describing temporal and spatial earthquake clustering. Its parameters have basic physical interpretations. Significant differences between regions may indicate different focal mechanisms of earthquakes and different local stress situations. The standard errors of parameter estimates in the ETAS model are thus important in determining the accuracy of particular estimates and in assessing whether differences between estimated parameters across different regions are significant. Our purpose is to investigate the accuracy of conventional standard error estimates for parameters in the ETAS model. We examine the uncertainties of parameter estimates for earthquake clustering models such as the epidemic-type aftershock sequence (ETAS) model. The standard errors are significant and cannot be ignored. We used simulations to explore the accuracy of conventional standard error estimates based on the Hessian matrix of the log-likelihood function of the ETAS model. These Hessian estimates are exact for problems with strictly linear dependence of predicted quantities on parameters, and reasonable for quasi-linear problems. But are ETAS models linear enough? We show that Hessian error estimates are not accurate when the observed space-time window is small, as is typical of those used in California. The standard errors for all parameter estimates introduced by magnitude errors in typical earthquake catalogs are found to be smaller than those introduced by choosing a finite time window, but neither effect is insignificant.
Intellectual Merit Point process models such as the epidemic-type aftershock sequence (ETAS) model have been widely used to analyze and describe seismic catalogs and to perform short-term forecasting. The standard errors of parameter estimates in the ETAS model are significant and cannot be ignored. We used simulations to explore the accuracy of conventional standard error estimates based on the Hessian matrix of the log-likelihood function of the ETAS model. We illustrate the use of simulation to estimate parameter uncertainty without restrictive assumptions and to show the effects on short term earthquake forecasting.
Broader Impacts In this project we trained grad student Qi Wang, who obtained his PhD based largely on work done in the project. In addition, we involved Prof. Rick Schoenberg of the UCLA Statistics Department in the project, beginning a fruitful interdisciplinary collaboration. Dr. Qi Wang went on to work for a company advising insurance and re-insurance providers on earthquake hazards, and he used the results of this work in his research there.
Exemplary Figure Figure 1. The ratio of the bias of the standard errors of parameters based on Hessian over the true value of the ETAS parameters as a function of time window length (years). SES is the simulation-based standard error of parameter estimates and SEH is the Hessian-based standard error of parameter estimates.