Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian nonparametric framework for spatio-temporal Hawkes processes using additive Gaussian processes for the prior distributions on the background rate and the triggering kernel. This additive structure enhances interpretability by decoupling temporal and spatial effects while maintaining high modelling flexibility across the entire spatio-temporal domain. To address scalability, we develop a sparse variational inference scheme based on the Gaussian variational family. Synthetic experiments demonstrate that the proposed method accurately recovers background and triggering structures, achieving superior performance compared to existing alternatives. When applied to real-world datasets, it achieves higher held-out log-likelihoods and reveals interpretable spatio-temporal structures of the self-excitation mechanism. Overall, the framework provides a flexible, scalable, interpretable, and uncertainty-aware approach for modelling complex excitation patterns in spatio-temporal event data.

翻译：现有的时空霍克斯过程模型通常依赖参数或半参数假设，限制了模型捕捉复杂内生性和外生性事件动态的能力。我们提出一种完全贝叶斯非参数框架用于时空霍克斯过程，通过为背景率和触发核的先验分布引入加性高斯过程。该加性结构通过解耦时间与空间效应增强了可解释性，同时在整个时空域内保持高建模灵活性。为解决可扩展性问题，我们开发了基于高斯变分族的稀疏变分推断方案。合成实验表明，所提方法能准确恢复背景与触发结构，相较于现有替代方案实现了更优性能。应用于真实数据集时，该方法获得了更高的留出对数似然值，并揭示了自激发机制中可解释的时空结构。总体而言，该框架为建模时空事件数据中的复杂激发模式提供了一种灵活、可扩展、可解释且具有不确定性感知能力的方法。