Parameter Estimation in the ETAS Model: Approximations and Novel Methods

Branching processes provide an accurate description of earthquake occurrence in the short term (days to a few weeks). Yet, the implementation of these models is not usually straightforward because of the difficulties in estimating the parameters. Indeed, log-likelihood estimation involves a spatial integral that cannot be analytically evaluated and is difficult to implement in numerical codes. Here we present a novel technique that allows for an accurate, stable, and relatively fast parameter inversion procedure. We study the efficiency of this technique using synthetic epidemic-type aftershock sequence catalogs with a set of parameters known a priori. Results show the efficiency of the novel technique and illustrate the limits of recently proposed approximations.