Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the nonlinear Hawkes process. Working within a Bayesian framework, model fitting is implemented through Markov chain Monte Carlo. This entails discussion of computation of the likelihood for such point patterns. Furthermore, for this class of models, we discuss strategies for model comparison. Using simulation, we illustrate how well we can distinguish these models from point pattern specifications with conditionally independent event times, e.g., Poisson processes. Specifically, we demonstrate that these models can correctly identify true relationships (i.e., excitation or inhibition/control). Then, we consider a novel extension of the log Gaussian Cox process that incorporates evolutionary behavior and illustrate that our model comparison approach prefers the evolutionary log Gaussian Cox process compared to simpler models. We also examine a real dataset consisting of violent crime events from the 11th police district in Chicago from the year 2018. This data exhibits strong daily seasonality and changes across the year. After we account for these data attributes, we find significant but mild self-excitation, implying that event occurrence increases the intensity of future events.

广义进化点过程提供了一类点过程模型，这些模型可以基于过程历史来激发或抑制。在这方面，我们提出了包括非线性霍克斯过程推广的建模。在贝叶斯框架内工作，通过马尔可夫链蒙特卡洛实现模型拟合。这就需要讨论计算这种点模式的可能性。此外，对于此类模型，我们讨论了模型比较的策略。通过仿真，我们说明了如何在条件独立的事件时间（例如泊松过程）下将这些模型与点模式规范区分开。具体而言，我们证明了这些模型可以正确识别真实的关系（即激发或抑制/控制）。然后，我们考虑了对数高斯考克斯过程的一种新颖扩展，它包含了进化行为，并说明我们的模型比较方法与简单模型相比，更喜欢对数高斯考克斯过程。我们还检查了一个真实的数据集，该数据集由2018年以来的芝加哥第11警察区的暴力犯罪事件组成。该数据显示出强劲的每日季节性和全年变化。在考虑了这些数据属性之后，我们发现了明显但温和的自激，这意味着事件的发生增加了未来事件的强度。我们还检查了一个真实的数据集，该数据集由2018年以来的芝加哥第11警察区的暴力犯罪事件组成。该数据显示出强劲的每日季节性和全年变化。在考虑了这些数据属性之后，我们发现了明显但温和的自激，这意味着事件的发生增加了未来事件的强度。我们还检查了一个真实的数据集，该数据集由2018年以来的芝加哥第11警察区的暴力犯罪事件组成。该数据显示出强劲的每日季节性和全年变化。在考虑了这些数据属性之后，我们发现了明显但温和的自激，这意味着事件的发生增加了未来事件的强度。