Variable selection for inhomogeneous spatio-temporal Poisson point processes

Spatio-temporal point pattern data are becoming prevalent in many scientific disciplines. We model the first-order intensity of spatio-temporal point pattern data, considering the intensity as a parametric log-linear function of spatial, temporal, and spatio-temporal covariates. Dealing with spatio-temporal covariates brings computational and methodological challenges compared to the purely spatial case. We extend regularisation methods to perform variable selection for spatial point processes to the spatio-temporal case to obtain parsimonious and more interpretable models. Using our proposed methodology, we conduct two simulation studies and examine an application to criminal activity in the Kennedy district of Bogota. In the application, we consider a spatio-temporal point pattern of crime locations and many spatial, temporal, and spatio-temporal covariates related to urban places, environmental factors, and further space-time factors. The intensity function of vehicle thefts is estimated, considering other crimes as covariate information. The proposed methodology offers a comprehensive approach for analysing spatio-temporal point pattern crime data, capturing complex relationships between covariates and crime occurrences over space and time.