论文标题
贝叶斯推断霍克斯过程
Bayesian inference for aggregated Hawkes processes
论文作者
论文摘要
霍克斯流程是一个自我激发的点过程，在建模地震，社交网络和股票市场中具有广泛的应用。既定的估计过程要求研究人员可以访问确切的时间戳记和空间信息。但是，可用的数据通常是圆形或汇总的。我们根据汇总数据制定了霍克斯过程参数的贝叶斯估计程序。我们的方法是针对时间，时空和相互激动人心的霍克斯过程开发的，在这些过程中，数据在离散的时间段和区域内可用。从理论上讲，我们表明，霍克斯过程的参数可以从一般规格下的汇总数据中识别。我们在存在一个或多个相互作用过程的情况下以及数据聚合的变化下，在各种模型规格下的模拟数据中证明了该方法。最后，我们研究了2007年2月至2008年6月的空袭和叛乱暴力事件的内部和交叉激发效应，每天汇总了一些数据。
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time stamps and spatial information. However, available data are often rounded or aggregated. We develop a Bayesian estimation procedure for the parameters of a Hawkes process based on aggregated data. Our approach is developed for temporal, spatio-temporal, and mutually exciting Hawkes processes where data are available over discrete time periods and regions. We show theoretically that the parameters of the Hawkes process are identifiable from aggregated data under general specifications. We demonstrate the method on simulated data under various model specifications in the presence of one or more interacting processes, and under varying coarseness of data aggregation. Finally, we examine the internal and cross-excitation effects of airstrikes and insurgent violence events from February 2007 to June 2008, with some data aggregated by day.
