Identification of Latent Structure in Spatio-Temporal Models of Violence

The modeling of violence, including terrorist activity, over space and time is often done using one of two broad classes of statistical models. Typically, the location of an event is modeled as a spatio-temporal point process and the latent structure is either modeled through a latent Gaussian process motivated by a log-Gaussian Cox process or through data dependency similar to a Hawkes process. The former is characterized through dependence in an unobserved latent Gaussian process, while the later assumes a data driven dependence in the data. While both techniques have been used successfully it remains unclear whether the processes are practically different from one another. In this manuscript, we demonstrate that in many situations, the most common statistic to characterize clustering in a process, Ripley's K function, cannot differentiate between the two processes and should not be used.