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

恐怖主义的威胁是一个紧迫的全球安全问题，每年发生数千起恐怖袭击，造成数万人死亡。分析以往恐怖事件的模式是研究人员了解恐怖主义及其决定因素的主要方式之一，从而使各国政府能够在未来制定更有效的反恐政策。然而，研究人员使用的大多数统计模型都不适合捕捉全球恐怖主义的复杂动态。例如，众所周知，恐怖主义行为往往会导致随后的恐怖行为。然而，目前对恐怖活动演变的理解仍然有限，受到一些方法的限制，这些方法要么假设事件独立，要么缺乏足够灵活的依赖模式。在这个项目中，私人投资机构计划推广这些统计方法，使其更适合分析全球恐怖主义，并帮助确定恐怖运动内部和之间更复杂的相互作用。该项目的结果最终将使政策制定者受益，并有助于政府遏制此类暴力的努力。PIS将为普通受众撰写项目成果的流行摘要，并通过培训研究生和开发课程将拟议的研究与教育结合起来。这个多学科项目的目标是在全球范围内开发具有灵活的非平稳时空强度函数的时空Hawkes过程模型。目前文献中发现的Hawkes过程模型通常是单变量的，仅定义在平面域上，不允许时空相互作用。PI将开发定义在球体表面的霍克斯过程模型，触发函数具有灵活的时空结构。具体的发展将包括时空非平稳性、不可分离性和不对称性。将对拟议模型进行多变量扩展，以同时模拟不同类型的袭击或多个恐怖团体的袭击。将研究通过数值计算海量全球数据的可能性的统计推断，以及点模式数据中时空结构的假设检验程序。建议的方法将被应用于对单个国家的单个恐怖组织以及全球恐怖主义模式的分析。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.