多元离散霍克斯过程的估计：在事件监测中的应用
Estimation of Multivariate Discrete Hawkes Processes: An Application to Incident Monitoring
AI总结：
本文提出多元带标记离散霍克斯过程的高效估计算法，用于法医精神病医院暴力事件建模，并证明其预测能力优于替代模型。
摘要：
霍克斯过程是一类自激点过程，用于对复杂现象进行建模。虽然霍克斯过程的大多数应用假设事件数据发生在连续时间中，但研究较少的离散时间版本在某些情况下更为适用。在这项工作中，我们开发了用于高效实现离散霍克斯过程的方法论。我们通过开发高效算法来评估对数似然函数及其梯度，其计算复杂度与事件数量呈线性关系。我们将这些方法扩展到一种特定形式的多元带标记离散霍克斯过程，并用它来对一家法医精神病医院内暴力事件的发生进行建模。我们问题的一个显著特征是由过程中的一个标记所捕捉的，即存在一个在整个医院都能听到的警报系统。当某个事件在性质上特别暴力并且需要呼叫其他工作人员前来协助时，就会响起警报。我们进行了详细分析，表明这种霍克斯过程的变体在预测能力方面能够优于替代模型。最后，我们解释了我们的发现并描述了其意义。
英文摘要：
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of the process is more appropriate in some situations. In this work, we develop methodology for the efficient implementation of discrete Hawkes processes. We achieve this by developing efficient algorithms to evaluate the log-likelihood function and its gradient, whose computational complexity is linear in the number of events. We extend these methods to a particular form of a multivariate marked discrete Hawkes process which we use to model the occurrences of violent events within a forensic psychiatric hospital. A prominent feature of our problem, captured by a mark in our process, is the presence of an alarm system which can be heard throughout the hospital. An alarm is sounded when an event is particularly violent in nature and warrants a call for assistance from other members of staff. We conduct a detailed analysis showing that such a variant of the Hawkes process manages to outperform alternative models in terms of predictive power. Finally, we interpret our findings and describe their implications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
