ETASbootstrap 0.2.0: A flexible R package for computing bootstrap confidence intervals for parameters in the space–time epidemic-type aftershock sequence model, with four case studies

Abstract

The space–time epidemic-type aftershock sequence (ETAS) model is a widely used tool for stochastic declustering of earthquake data catalogs and short-term aftershock forecasting. However, confidence intervals derived from asymptotic standard errors (ASEs) of parameter estimates based on maximum-likelihood theory can sometimes be misleading and it was recently suggested to use bootstrap confidence intervals instead (Dutilleul et al., 2024). The ETASbootstrap package was developed to facilitate the use of the bootstrap resampling procedure and its associated confidence intervals for a direct comparison with asymptotic ones. In this paper, the statistical underpinnings of the package are first presented, including the space–time ETAS model with its multiple parameters, the importance of edge effects, and the bootstrapping algorithm. Then, three earthquake data catalogs (Japan, Italy, Iran) are used as input to ETASbootstrap 0.2.0, which is more flexible regarding the shape of spatial windows than the original version. In all cases, a discrepancy was observed between bootstrap and asymptotic confidence intervals for some of the space–time ETAS model parameters. It was possible to relate this discrepancy to the presence of outliers and a resulting lack of normality, which compromised the asymptotic approximation of the variability of the maximum-likelihood estimates (ML estimates). The results suggest that the two types of confidence intervals should be used in practice, especially for earthquake data catalogs of moderate size.