Quantile temporal graph convolutional networks and Bayesian hierarchical spatiotemporal models for crime risk forecasting and hotspot identification

Granular spatio-temporal forecasting of socioeconomic risks, particularly regional crime dynamics, is crucial for formulating targeted public policies and optimizing resource allocation under fiscal constraints. This study presents a comparative framework that benchmarks deep probabilistic graph architectures against Bayesian hierarchical models across 52 administrative districts in South Africa, leveraging a unique multi-year dataset from the Governance, Public Safety, and Justice Survey (GPSJS) spanning 2018/19 to 2023/24. Specifically, we evaluate a novel Quantile Temporal Graph Convolutional Network (Quantile TGCN), which integrates spatio-temporal graph convolutions with pinball-loss optimization to generate distribution-free, calibrated prediction intervals. This model is contrasted with a deterministic Standard TGCN baseline and Bayesian spatio-temporal models fitted via Integrated Nested Laplace Approximation (INLA), incorporating Besag-York-Mollié (BYM2) spatial priors under both Gamma and log-normal observation models. The evaluation criteria include out-of-sample point forecast accuracy, residual bias profiles, prediction interval calibration, and the ability to rank high-risk spatial hotspots under strict allocation constraints. Contrary to expectations that more complex architectures would yield superior predictive performance, the Bayesian INLA specifications, particularly the log-normal BYM2 model, demonstrated lower out-of-sample errors and stronger discrimination of high-risk districts. Notably, the Quantile TGCN excels in producing well-calibrated, distribution-free prediction intervals, thus offering valuable insights for granular risk monitoring and evidence-based governance in emerging economies. This comparative approach contributes to the development of robust diagnostic tools for socioeconomic risk assessment and intervention planning.