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A class of spatially correlated self-exciting statistical models
Spatial Statistics ( IF 2.3 ) Pub Date : 2021-02-12 , DOI: 10.1016/j.spasta.2021.100493
Nicholas J. Clark , Philip M. Dixon

The statistical modeling of multivariate count data observed on a space–time lattice has generally focused on using a hierarchical modeling approach where space–time correlation structure is placed on a continuous, latent, process. The count distribution is then assumed to be conditionally independent given the latent process. However, in many real-world applications, especially in the modeling of criminal or terrorism data, the conditional independence between the count distributions is inappropriate. In this manuscript we propose a class of models that capture spatial variation and also account for the possibility of data model dependence. The resulting model allows both data model dependence, or self-excitation, as well as spatial dependence in a latent structure. We demonstrate how second-order properties can be used to characterize the spatio-temporal process and how misspecification of error may inflate self-excitation in a model. Finally, we give an algorithm for efficient Bayesian inference for the model demonstrating its use in capturing the spatio-temporal structure of burglaries in Chicago from 2010–2015.



中文翻译:

一类与空间相关的自激统计模型

在时空格上观察到的多元计数数据的统计建模通常集中在使用分层建模方法上,其中时空相关结构放置在连续的,潜在的过程中。然后假定给定潜在过程,则计数分布是条件独立的。但是,在许多实际应用中,尤其是在犯罪数据或恐怖主义数据的建模中,计数分布之间的条件独立性是不合适的。在本手稿中,我们提出了一类模型,这些模型可以捕获空间变化并考虑数据模型依赖性的可能性。结果模型允许数据模型依赖或自我激励,以及潜在结构中的空间依赖。我们演示了如何使用二阶属性来描述时空过程,以及错误的错误指定如何使模型中的自激膨胀。最后,我们为模型提供了一种有效的贝叶斯推断算法,展示了该算法在捕获2010-2015年芝加哥盗窃案的时空结构中的应用。

更新日期:2021-02-23
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