Spatio-temporal log-Gaussian Cox processes on eartquake events

In this paper we aim at studying some extensions of complex space-time models,useful for the description of earthquake data. In particular we want to focus on theLog-Gaussian Cox Process (LGCP) model estimation approach, with some resultson global informal diagnostics. Indeed, in our opinion the use of Cox processes thatare natural models for point process phenomena that are environmentally drivencould be a new approach for the description of seismic events. These models canbe useful in estimating the intensity surface of a spatio-temporal point process, inconstructing spatially continuous maps of earthquake risk from spatially discretedata, and in real-time seismic activity surveillance. Moreover, covariate informationvarying in space-time can be considered into the LGCP model, providing complexmodels useful for a proper description of seismic events. LGCP is a Cox process witha stochastic intensity function, depending on a Gaussian process. This constructionhas some advantages, related to the multivariate Normal distribution features, sincethe moment properties of the intensity function are inherited by the Cox process. Inparticular, both estimation and diagnostics, can deal with some higherorder properties,expressed for instance by the intensity and the pair correlation function of theLGCP.