Variable selection for spatio-temporal conditionally Poisson point processes

Spatio-temporal point pattern data are becoming prevalent in many scientific disciplines. We consider a sequence of spatial point processes where each point process is Poisson given the past. We model the conditional first-order intensity function of each point process as a parametric log-linear function of spatial, temporal, and spatio-temporal covariates that may depend on previous point patterns. Dealing with spatio-temporal covariates brings computational and methodological challenges compared to the purely spatial case. We extend regularisation methods for spatial point process variable selection to obtain parsimonious and interpretable models in the considered spatio-temporal case. 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 data of crime locations and a number of 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.