Detecting local regions of change in high-dimensional criminal or terrorist point processes

A method is presented for detecting changes to the distribution of a criminal or terrorist point process between two time periods using a non-model-based approach. By treating the criminal/terrorist point process as an intelligent site selection problem, changes to the process can signify changes in the behavior or activity level of the criminals/terrorists. The locations of past events and an associated vector of geographic, environmental, and socio-economic feature values are employed in the analysis. By modeling the locations of events in each time period as a marked point process, we can then detect differences in the intensity of each component process. A modified PRIM (patient rule induction method) is implemented to partition the high-dimensional feature space, which can include mixed variables, into the most likely change regions. Monte Carlo simulations are easily and quickly generated under random relabeling to test a scan statistic for significance. By detecting local regions of change, not only can it be determined if change has occurred in the study area, but the specific spatial regions where change occurs is also identified. An example is provided of breaking and entering crimes over two-time periods to demonstrate the use of this technique for detecting local regions of change. This methodology also applies to detecting regions of differences between two types of events such as in case–control data.