A Fully Non-separable Log-Gaussian Cox Process to Model Forest Fires

Log-Gaussian Cox processes provide a flexible class of spatio-temporal models which allow the description of a wide variety of complex dependence structures in form of clustering in point patterns. The clustering effect observed in these patterns can be described by the inclusion of random heterogeneities through an unobservable Gaussian process affecting the intensity function. Typically, spatio-temporal point patterns have been modeled considering a separable structure in space and time, following pragmatic reasons, that in many cases were non-realistic. Here, we overcome this way of proceeding by proposing a model for the first-order intensity function that combines a non-separable structure for the large-scale effects, with a non-separable correlation structure for the underlying random field that outlines small-scale effects. This methodology allows to underpin the interaction of the spatial and temporal components, while better mimicking the intrinsic behavior of the events in space and time. Global and local weighted second-order statistics are used to assess the improvement in the predictive performance of the proposed model compared to that obtained with a separable assumption. We use our modeling strategy to analyze the behavior of forest fires in Nepal, where global trends in the intensity function are modeled using external covariate information.