BAYESIAN MITIGATION OF SPATIAL COARSENING FOR A HAWKES MODEL APPLIED TO GUNFIRE, WILDFIRE AND VIRAL CONTAGION.

IF 1.3 4区 数学 Q2 STATISTICS & PROBABILITY Annals of Applied Statistics Pub Date : 2022-03-01 Epub Date: 2022-03-28 DOI:10.1214/21-aoas1517
Andrew J Holbrook, Xiang Ji, Marc A Suchard
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Abstract

Self-exciting spatiotemporal Hawkes processes have found increasing use in the study of large-scale public health threats, ranging from gun violence and earthquakes to wildfires and viral contagion. Whereas many such applications feature locational uncertainty, that is, the exact spatial positions of individual events are unknown, most Hawkes model analyses to date have ignored spatial coarsening present in the data. Three particular 21st century public health crises-urban gun violence, rural wildfires and global viral spread-present qualitatively and quantitatively varying uncertainty regimes that exhibit: (a) different collective magnitudes of spatial coarsening, (b) uniform and mixed magnitude coarsening, (c) differently shaped uncertainty regions and-less orthodox-(d) locational data distributed within the "wrong" effective space. We explicitly model such uncertainties in a Bayesian manner and jointly infer unknown locations together with all parameters of a reasonably flexible Hawkes model, obtaining results that are practically and statistically distinct from those obtained while ignoring spatial coarsening. This work also features two different secondary contributions: first, to facilitate Bayesian inference of locations and background rate parameters, we make a subtle yet crucial change to an established kernel-based rate model, and second, to facilitate the same Bayesian inference at scale, we develop a massively parallel implementation of the model's log-likelihood gradient with respect to locations and thus avoid its quadratic computational cost in the context of Hamiltonian Monte Carlo. Our examples involve thousands of observations and allow us to demonstrate practicality at moderate scales.

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应用于枪火、野火和病毒传染的霍克斯模型的空间粗化的贝叶斯缓解。
自激时空霍克斯过程越来越多地应用于大规模公共健康威胁的研究,从枪支暴力和地震到野火和病毒传染。许多此类应用都具有位置不确定性,即单个事件的确切空间位置是未知的,而迄今为止的大多数霍克斯模型分析都忽略了数据中存在的空间粗化现象。21 世纪的三个特殊公共卫生危机--城市枪支暴力、农村野火和全球病毒传播--呈现出定性和定量不同的不确定性机制,表现出:(a)不同的集体空间粗化幅度,(b)均匀和混合幅度的粗化,(c)不同形状的不确定性区域,以及(d)分布在 "错误 "有效空间内的定位数据。我们以贝叶斯方式对这些不确定性进行了明确建模,并将未知位置与合理灵活的霍克斯模型的所有参数一起进行了联合推断,得到的结果与忽略空间粗化时得到的结果在实践和统计上都截然不同。这项工作还有两个不同的次要贡献:首先,为了便于对位置和背景速率参数进行贝叶斯推断,我们对一个已建立的基于核的速率模型做了一个微妙而关键的改动;其次,为了便于在规模上进行同样的贝叶斯推断,我们开发了一种大规模并行实施该模型关于位置的对数似然梯度的方法,从而避免了在汉密尔顿蒙特卡罗背景下的二次计算成本。我们的例子涉及成千上万的观测数据,使我们能够证明在中等规模下的实用性。
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来源期刊
Annals of Applied Statistics
Annals of Applied Statistics 社会科学-统计学与概率论
CiteScore
3.10
自引率
5.60%
发文量
131
审稿时长
6-12 weeks
期刊介绍: Statistical research spans an enormous range from direct subject-matter collaborations to pure mathematical theory. The Annals of Applied Statistics, the newest journal from the IMS, is aimed at papers in the applied half of this range. Published quarterly in both print and electronic form, our goal is to provide a timely and unified forum for all areas of applied statistics.
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