Exploring and Modeling Fire Department Emergencies with a Spatio-Temporal Marked Point Process

Résumé

We examine a database of fire department emergencies in the surroundings of the city of Toulouse during the year 2004,using methods of statistical analysis for spatial point patterns. Firemen emergencies are characterized by their positions anddifferent features (time, duration, type,…) that one can model as a spatio-temporal marked point process. For our study,we consider the following characteristics of firemen emergencies: positions, time of occurrences and marks which take intoaccount the duration and the number of firemen involved. We use graphical methods to explore the structure of theunderlying spatial point process with a final objective of choosing a suitable model for future work. We first review the basicconcepts and methods used in the paper. Considering the marginal spatio-temporal point pattern, we propose to evaluate theimportance of the variation of intensity over time in comparison with spatial variation and to test the dependence betweenpositions and time. Afterwards, we conduct an exploratory analysis of the marks to test their dependence with positions aswell as their dependence with time. Our resulting framework of independence allows us to explore the dependence betweencategories in order to test the random labeling hypothesis. Then, under the hypothesis of random labeling and invariance intime which have been established in the first two parts, we fit a spatial point process model to the unmarked spatial pointpattern aggregated over the whole year. Finally, we analyze the goodness-of-fit of our models by exploring the first andsecond order characteristics of simulations from the fitted models. Throughout this article, the exploratory analysis is madeusing mainly the R package spatstat. An exposure to point processes is useful but not indispensable for understanding theexposition.