Non‐Parametric Spatio‐Temporal Self‐Exciting Point Process Model With Gaussian Mixture Kernels for Crime Event Analysis

Crime studies have garnered significant interest in recent times due to the rising rate of criminal activities. Understanding the spatial and temporal clustering of crime events such as burglary, robbery and theft has become essential. In this study, we propose a non‐parametric self‐exciting point process model with Gaussian mixture kernels (GMKs), along with a truncation technique for the intensity function. The proposed GMK can give accurate estimation while simultaneously reducing computational time. We first evaluate the performance of the proposed model using simulated data. Subsequently, we demonstrate its applicability in analysing the clustering patterns of theft in Philadelphia and robbery in Chicago. Residual analysis is employed as a diagnostic tool to assess the effectiveness of the model. To further evaluate its predictive capability, we generate 3‐day forecasts, illustrating the potential of the self‐exciting point process in capturing the clustering behaviour of these crime types.