ATD: Global Terrorism Threat Detection by Nonstationary, Spatio-Temporal Hawkes Process Models

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The threat of terrorism is a pressing global security concern, with thousands of terror attacks producing tens of thousands of deaths annually. Analyzing patterns of prior terror events is one of the primary ways researchers can learn about terrorism and its determinants, thereby enabling governments to craft more effective counter-terrorism policy in the future. Yet, most statistical models used by researchers are ill-suited to capture the complex dynamics of global terrorism. For example, it is known that acts of terrorism often produce subsequent acts of terror. However, current understanding of the evolution of terror campaigns remains limited and constrained by methods which either assume independence across events or lack sufficiently flexible models of dependence. In this project, the PIs plan to generalize these statistical approaches to make them better suited for the analysis of global terrorism, and to help identify more complex interactions within and across terror campaigns. The results of this project will ultimately benefit policy makers and aid government efforts to curb such violence. The PIs will author popular summaries of the project results for general audiences, and integrate the proposed research with education through training graduate students and developing courses. This multidisciplinary project aims to develop spatio-temporal Hawkes process models on a global scale with flexible nonstationary spatio-temporal intensity functions. Current Hawkes process models found in the literature are often univariate, defined only on the planar domain, and do not permit spatio-temporal interactions. The PIs will develop Hawkes process models defined on the surface of a sphere with a flexible spatio-temporal structure in the triggering function. Specific developments will include spatio-temporal nonstationarity, non-separability, and asymmetry. Multivariate extensions of the proposed models will be pursued to simultaneously model varied attack types or attacks by multiple terrorist groups. Statistical inference with numerical computation of the likelihood for massive global data, and procedures for hypothesis tests of spatio-temporal structures in point pattern data will be studied. Proposed methods will be applied to the analysis of individual terrorist groups in single countries, as well as global terrorism patterns.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.