Abstract
etasFLP is an R package which fits an epidemic type aftershock sequence (ETAS) model to an earthquake catalog; non-parametric background seismicity can be estimated through a forward predictive likelihood approach, while parametric components of triggered seismicity are estimated through maximum likelihood; estimation steps are alternated until convergence is obtained and for each event the probability of being a background event is estimated. The package includes options which allow its wide use. Methods for plot, summary and profile are defined for the main output class object. The paper provides examples of the package's use with description of the underlying R and Fortran routines.
Highlights
A reliable estimation of the conditional intensity function is crucial in the description of seismic data through a space time point process
Often the conditional intensity function presents a superposition of a parametric component over a non-parametric component, e.g., in the epidemic type aftershock sequence (ETAS) model (Ogata 1988), widely used in statistical seismology
If we want to predict large earthquakes in presence of clusters of aftershocks, these may complicate the statistical analysis of the background seismic activity (Adelfio, Chiodi, De Luca, Luzio, and Vitale 2006) so it could be useful to study the features of independent events separately from the study of the strongly correlated ones in order to describe the seismicity of an area in space, time and magnitude domains
Summary
A reliable estimation of the conditional intensity function is crucial in the description of seismic data through a space time point process. Zhuang, Ogata, and Vere-Jones (2002) proposed a stochastic method ( implemented as etasFLP: Mixed Estimation in R for Earthquakes’ Description an option in the package etasFLP) which associates a probability that each event is either a background event or an offspring generated by other events, based on the ETAS model as in a latent class cluster model. In Adelfio and Chiodi (2013, 2015a), we classified events according to their probability of being a background or an offspring event, as proposed by Zhuang et al (2002), and estimated the space-time intensity of the generating point process of the different components by mixing non-parametric and parametric approaches, applying a forward predictive likelihood estimation approach to semi-parametric models (Chiodi and Adelfio 2011; Adelfio and Chiodi 2015a).
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