To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation.

中文翻译：

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伦敦的盗窃案：来自统计异质空间点过程的见解

为了获得有关伦敦盗窃罪的操作见解，我们考虑估计协变量对空间点模式强度的影响。受犯罪行为的局部属性的启发，我们从混合建模文献中提出了广义线性模型混合的空间扩展。提出的贝叶斯模型是泊松广义线性模型的有限混合，因此每个位置都有可能被分配给其中一个组。每个组的特征在于回归系数，我们随后将其用于解释协变量的局部影响。通过使用研究区域的块结构，我们的方法可以指定附近位置之间的空间依赖性。