Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime
Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime
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DOI：
10.1016/j.csda.2019.106850
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发表时间：
2020-04-01
影响因子：
1.8
通讯作者：
Delahaies, Sylvain
中科院分区：
文献类型：
--
作者：
Santitissadeekorn, Naratip;Lloyd, David J. B.;Delahaies, Sylvain
主要的焦点是一个顺序的数据同化方法，以非齐次泊松过程建模的计数数据。特别是，类似于扩展卡尔曼滤波器的二次逼近技术被应用于开发一种次优的离散时间滤波算法，称为扩展泊松-卡尔曼滤波器（ExPKF），其中只有均值和协方差通过泊松似然函数使用计数数据顺序更新。在几个已知真实解的合成实验中，对ExPKF的性能进行了研究。在数值算例中，ExPKF提供了一个很好的“真实”后验均值估计，在非常大的样本量限制下，粒子滤波（PF）算法可以很好地逼近它。此外，实验表明，ExPKF算法可以方便地用于跟踪参数变化，而另一方面，最大似然估计（MLE）等非滤波框架则需要对变化点进行统计测试或实现时变参数。最后，为了在实际数据上验证该模型，使用ExPKF来近似城市犯罪强度和自激犯罪模型参数的不确定性。芝加哥警察局的CLEAR（公民执法分析和报告）系统数据被用作单变量和多变量Hawkes模型的案例研究。通过滤波强度，可以获得由Kolmogorov-Smirnov （KS）统计量测量的拟合优度的改进。使用过滤强度来提高警察巡逻优先级的潜力也得到了测试。通过与基于mle衍生的强度和历史频率的优先级进行比较，结果表明它们之间的差异不显著。虽然过滤器是在城市犯罪的背景下开发和测试的，但它有可能对其他应用领域的数据同化作出贡献。爱思唯尔B.V.版权所有
The primary focus is a sequential data assimilation method for count data modelled by an inhomogeneous Poisson process. In particular, a quadratic approximation technique similar to the extended Kalman filter is applied to develop a sub-optimal, discrete time, filtering algorithm, called the extended Poisson-Kalman filter (ExPKF), where only the mean and covariance are sequentially updated using count data via the Poisson likelihood function. The performance of ExPKF is investigated in several synthetic experiments where the true solution is known. In numerical examples, ExPKF provides a good estimate of the "true" posterior mean, which can be well-approximated by the particle filter (PF) algorithm in the very large sample size limit. In addition, the experiments demonstrate that the ExPKF algorithm can be conveniently used to track parameter changes: on the other hand, a non-filtering framework such as a maximum likelihood estimation (MLE) would require a statistical test for change points or implement time varying parameters. Finally, to demonstrate the model on real-world data, the ExPKF is used to approximate the uncertainty of urban crime intensity and parameters for self-exciting crime models. The Chicago Police Department's CLEAR (Citizen Law Enforcement Analysis and Reporting) system data is used as a case study for both univariate and multivariate Hawkes models. An improved goodness of fit measured by the Kolmogorov-Smirnov (KS) statistics is achieved by the filtered intensity. The potential of using filtered intensity to improve police patrolling prioritisation is also tested. By comparing with the prioritisation based on MLE-derived intensity and historical frequency, the result suggests an insignificant difference between them. While the filter is developed and tested in the context of urban crime, it has the potential to make a contribution to data assimilation in other application areas. Crown Copyright (C) 2019 Published by Elsevier B.V. All rights reserved.