Space-time cluster identification in point processes

The authors propose a new type of scan statistic 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. Their method is based only on point patterns for cases; it does not require any specific knowledge of the underlying population. The authors propose to scan the three-dimensional space with a score test statistic under the null hypothesis that the underlying point process is an inhomogeneous Poisson point process with space and time separable intensity. The alternative is that there are one or more localized space-time clusters. Their method has been implemented in a computationally efficient way so that it can be applied routinely. They illustrate their method with space-time crime data from Belo Horizonte, a Brazilian city, in addition to presenting a Monte Carlo study to analyze the power of their new test.