Bootstrapping for parameter uncertainty in the space–time epidemic-type aftershock sequence model

Abstract

SUMMARY This paper proposes the use of the parametric bootstrap as a simple way of obtaining reliable confidence intervals for the parameters in the space–time epidemic-type aftershock sequence (ETAS) model. Using an earthquake data catalogue spanning almost 20 yr of seismic activity in the Pacific Ocean off the shores of Vancouver Island (British Columbia, Canada), the authors show through simulation that the confidence intervals based on asymptotic maximum-likelihood theory can sometimes be misleading. In contrast, confidence intervals based on empirical quantiles from bootstrap samples have reliable nominal coverage, provided that edge effects are properly taken into account, both in the bootstrap procedure and in simulation studies. An R package called ETASbootstrap, developed by the authors, facilitates the use of this resampling procedure.