Self-exciting point processes have been proposed as models for the location of criminal events in space and time. Here we consider the case where the triggering function is isotropic and takes a non-parametric form that is determined from data. We pay special attention to normalisation issues and to the choice of spatial distance measure, thereby extending the current methodology. After validating these ideas on synthetic data, we perform inference and prediction tests on public domain burglary data from Chicago. We show that the algorithmic advances that we propose lead to improved predictive accuracy.

中文翻译：

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使用具有各向同性触发的自激点过程模拟芝加哥盗窃案

自激点过程已被提出作为在空间和时间上定位犯罪事件的模型。在这里，我们考虑触发函数是各向同性的并且采用由数据确定的非参数形式的情况。我们特别关注归一化问题和空间距离度量的选择，从而扩展了当前的方法。在对合成数据验证了这些想法之后，我们对来自芝加哥的公共领域盗窃数据进行了推理和预测测试。我们表明，我们提出的算法进步可以提高预测准确性。