Some extensions in space-time LGCP: application to earthquakedata

In this paper we aim at studying some extensions of complex space-time models, useful for the descriptionof earthquake data. In particular we want to focus on the Log-Gaussian Cox Process (LGCP, [1]) model estimationapproach, with some results on global informal diagnostics. Indeed, in our opinion the use of Cox processes thatare natural models for point process phenomena that are environmentally driven could be a new approach for thedescription of seismic events. These models can be useful in estimating the intensity surface of a spatio-temporal pointprocess, in constructing spatially continuous maps of earthquake risk from spatially discrete data, and in real-timeseismic activity surveillance. Moreover, covariate information varying in space-time can be considered into the LGCPmodel, providing complex models useful for a proper description of seismic events. LGCP is a Cox process withΛ = expS(x), where S is a Gaussian process. This construction has some advantages, related to the multivariateNormal distribution features, since the moment properties Λ(x) are inherited by the Cox process. In particular, bothestimation and diagnostics, can deal with some higherorder properties [2], expressed for instance by the intensity andthe pair correlation function of the LGCP.