June 2024 Flexible multivariate spatiotemporal Hawkes process models of terrorism
Mikyoung Jun, Scott Cook
Author Affiliations +
Ann. Appl. Stat. 18(2): 1378-1403 (June 2024). DOI: 10.1214/23-AOAS1839


We develop flexible multivariate spatiotemporal Hawkes process models to analyze patterns of terrorism. Previous applications of point process methods to political violence data mainly utilize temporal Hawkes process models, neglecting spatial variation in these attack patterns. This limits what can be learned from these models, as any effective counter-terrorism strategy requires knowledge on both when and where attacks are likely to occur. Even the existing work on spatiotemporal Hawkes processes imposes restrictions on the triggering function that are not well-suited for terrorism data. Therefore, we generalize the structure of the spatiotemporal triggering function considerably, allowing for nonseparability, nonstationarity, and cross-triggering (across multiple terror groups). To demonstrate the utility of our models, we analyze two samples of real-world terrorism data: Afghanistan (2002–2013) as a univariate analysis and Nigeria (2009–2017) as a bivariate analysis. Jointly, these two studies demonstrate that our generalized models outperform standard Hawkes process models, besting widely-used alternatives in overall model fit and revealing spatiotemporal patterns that are, by construction, masked in these models (e.g., increasing dispersion in cross-triggering over time).

Funding Statement

The authors acknowledge support by NSF Grants DMS-1925119 and DMS-2123247. Mikyoung Jun also acknowledges support by NIH Grant P42ES027704.


The authors would like to thank the anonymous referees, an Associate Editor, and the Editor for their constructive comments that improved the quality of this paper significantly.


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Mikyoung Jun. Scott Cook. "Flexible multivariate spatiotemporal Hawkes process models of terrorism." Ann. Appl. Stat. 18 (2) 1378 - 1403, June 2024. https://doi.org/10.1214/23-AOAS1839


Received: 1 October 2022; Revised: 1 October 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1839

Keywords: GTD , Hawkes processes , multivariate point process , spatiotemporal point patterns , terrorism

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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