We develop a Bayesian modeling framework to address a pressing real-life problem faced by the police in tackling insurgent gangs. Unlike criminals associated with common crimes such as robbery, theft or street crime, insurgent gangs are trained in sophisticated arms and strategise against the government to weaken its resolve. They are constantly on the move, operating over large areas causing damage to national properties and terrorizing ordinary citizens. Different from the more commonly addressed problem of modeling crime-events, our context requires that an approach be formulated to model the movement of insurgent gangs, which is more valuable to the police forces in preempting their activities and nabbing them. This paper evolved as a collaborative work with the Indian police to help augment their tactics with a systematic method, by integrating past data on observed gang-locations with the expert knowledge of the police officers. A methodological challenge in modeling the movement of insurgent gangs is that the data on their locations is incomplete, since they are observable only at some irregularly separated time-points. Based on a weighted kernel density formulation for temporal data, we analytically derive the closed form of the likelihood, conditional on incomplete past observed data. Building on the current tactics used by the police, we device an approach for constructing an expert-prior on gang-locations, along with a sequential Bayesian procedure for estimation and prediction. We also propose a new metric for predictive assessment that complements another known metric used in similar problems.

翻译：我们构建了一个贝叶斯建模框架，以解决警方在打击叛乱团伙时面临的紧迫现实问题。与抢劫、盗窃或街头犯罪等普通犯罪中的犯罪分子不同，叛乱团伙经过复杂武器训练，并以削弱政府决心为目标进行战略对抗。他们不断移动，在广阔区域活动，破坏国家财产并恐吓普通民众。与更常见的犯罪事件建模问题不同，我们的问题需要建立一种针对叛乱团伙移动轨迹的建模方法——这对警方预判其行动并实施抓捕具有更高价值。本文通过与印度警方的合作研究，将观测到的团伙位置历史数据与警务专家的专业知识相结合，提出了一套系统化方法以增强其战术效能。建模叛乱团伙移动轨迹面临的方法学挑战在于：位置数据具有不完整性——我们仅能在某些不规则间隔的时间点观测到他们。基于时间数据的加权核密度公式，我们解析推导出以过去不完整观测数据为条件下的似然函数闭式解。在现有警方战术基础上，我们设计了一种构建团伙位置专家先验分布的方法，并建立了用于估计与预测的序贯贝叶斯流程。最终，我们提出了一种新的预测评估指标，该指标可与类似问题中使用的已知度量方法形成互补。