Bayesian and Non Parametric Estimation of ETAS Models Applied to Seismic Recurrence in Ecuador 2016

In this paper our purpose is to analyze, from the Bayesian point of view, the occurrence rate of earthquakes in Ecuador since March 2016 to July 16, 2016. We implemented in Stan language the ETAS models, starting with the purely temporal model, then considering the magnitudes, and later the spatio-temporal models (both isotropic and anisotropic), and finally the hypo-central model. We introduced the use of Welzl algorithm to evaluate the log-likelihood of the occurrence rate for spatio-temporal models. We conducted simulations by extracting values from the a posteriori distributions of the models parameters, to obtain estimations of the accumulated number of earthquakes (with magnitude greater than a threshold) and the behaviour of inter-time events. The estimations are validated with the observed from July 16 2016 to September 2016.