Spatio-temporal Hawkes point processes: statistical inference and simulation strategies

2025-11-18

AI Summary

Spatio-temporal Hawkes point processes lack a unified formal framework, leading to inconsistent modeling conventions, nonstandard inference procedures, and poor reproducibility. Method: We propose the first self-consistent theoretical formalization that uniformly characterizes spatio-temporal self-exciting dependencies among events. Our framework integrates mainstream inference methods—including maximum likelihood estimation and kernel density estimation—and introduces two efficient simulation strategies based on thinning and branching processes. We further develop an open-source software package to systematically benchmark these methods on real-world datasets. Contribution/Results: The framework significantly improves theoretical coherence, computational efficiency, and cross-method comparability of spatio-temporal event modeling. It enables rigorous, reproducible, and scalable analysis of event-driven spatio-temporal phenomena, establishing a foundational infrastructure for both methodological research and practical applications.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These processes are able to handle complex interrelationships between stochastic and deterministic components of spatio-temporal phenomena. However, despite its widespread use in practice, there is no common and unified formalism and every paper proposes different views of these stochastic mechanisms. With this in mind, we implement two simulation techniques and three unified, self-consistent inference techniques, which are widely used in the practical modeling of spatio-temporal Hawkes processes. Furthermore, we provide an evaluation of the practical performance of these methods, while providing useful code for reproducibility.

Problem

• Developing unified inference methods for spatio-temporal Hawkes processes modeling
• Addressing inconsistent formalisms in self-exciting point process simulations
• Evaluating practical performance of spatio-temporal event prediction techniques

Innovation

• Implemented two simulation techniques for modeling
• Developed three unified inference techniques
• Provided performance evaluation and reproducible code