Modeling wildfires via marked spatio-temporal Poisson processes

From a statistical viewpoint, characteristics such as ignition time, location and duration are relevant components for wildfire modeling. The observed ignition sites and starting times constitute a space-time point pattern, and a natural framework to model this type of data is via point processes. In this work, we propose a marked Poisson process to model fire patterns in space-time, considering durations as marks. The collected data correspond to fires observed in the Valencian Community, Spain, between 2010 and 2015. The methodology relies on writing the intensity function of such a process, jointly for starting times, locations and durations, as a weighted Dirichlet process mixture model. A particular choice of the kernel that determines such mixture was made, compatible with data features. We conducted posterior inference on some characteristics of interest for understanding wildfire behavior, showing high flexibility to emulate data patterns.