Atlanta Gun Violence Modeling via Nonstationary Spatio-Temporal Point Processes

Analysis of gun violence in the United States has utilized various models based on spatio-temporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban environments, which can be effectively represented using the self-excitatory spatio-temporal Hawkes process. The Hawkes process and its variants have been successful in modeling self-excitatory events, including earthquakes, disease outbreaks, financial market movements, neural activity, and the viral spread of memes on social networks. However, existing Hawkes models applied to gun violence often rely on simplistic stationary kernels, which fail to account for the complex, non-homogeneous spread of influence and impact over space and time. To address this limitation, we adopt a non-stationary spatio-temporal point process model that incorporates a neural network-based kernel to better represent the varied correlations among events of gun violence. Our study analyzes a comprehensive dataset of approximately 16,000 gunshot events in the Atlanta metropolitan area from 2021 to 2023. The cornerstone of our approach is the innovative non-stationary kernel, designed to enhance the model&s;s expressiveness while preserving its interpretability. This approach not only demonstrates strong predictive performance but also provides insights into the spatio-temporal dynamics of gun violence and its propagation within urban settings.