An Early Warning System for Space-Time Cluster Detection

Abstract. A new topic of great relevance and concern has been the design of efficient early warning systems to detect as soon as possible the emergence of spatial clusters. In particular, many applications involving spatial events recorded as they occur sequentially in time require this kind of analysis, such as fire spots in forest areas as in the Amazon, crimes occurring in urban centers, locations of new disease cases to prevent epidemics, etc. We propose a statistical method to test for the presence of space-time clusters in point processes data, when the goal is to identify and evaluate the statistical significance of localized clusters. It is based on scanning the threedimensional space with a score test statistic under the null hypothesis that the point process is an inhomogeneous Poisson point process with space and time separable first order intensity. We discuss an algorithm to carry out the test and we illustrate our method with space-time crime data from Belo Horizonte, a large Brazilian city.