Separability Testing for Point Processes with Covariates and An Application to Wildfire Hazard Assessment

Chien-Hsun Chang

In modeling marked point processes, it is typically assumed that marks are separable from the spatial-temporal coordinates. Tests have been proposed in the simple marked point process case to investigate the separability of the mark distribution. These tests are here extended to the case of a marked point process with covariates. The extension is not trivial, and covariates must be treated in a fundamentally different way than marks and coordinates of the process, especially when covariates are not uniformly distributed. Solutions are proposed to the problem of how to proceed when the separability hypothesis is rejected. An application of separable marked point process models with covariates is given to the assessment of the Burning Index in predicting wildfire activity. An examination of the Los Angeles County data reveals that the Burning Index predicts poorly compared to simple alternatives using just a few weather variables.