A multi-scale area-interaction model for spatio-temporal point patterns

Models for fitting spatio-temporal point processes should incorporate spatio-temporal inhomogeneity and allow for different types of interaction between points (clustering or regularity). This paper proposes an extension of the spatial multi-scale area-interaction model to a spatio-temporal framework. This model allows for interaction between points at different spatio-temporal scales and for the inclusion of covariates. We present a simulation study and fit the new model to varicella cases registered during 2013 in Valencia, Spain.