We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is possible through the decomposition of the joint distribution of marks and times that allows to separately specify the conditional distribution of marks given the filtration of the process and the current time. We develop a Bayesian framework for the inference and prediction from this family of marked point processes that can naturally accommodate process and point-specific covariate information to drive cross-excitations, offering wide flexibility and applicability in the modelling of real-world processes. The framework is used here for the modelling of in-game event sequences from association football, resulting not only in inferences about previously unquantified characteristics of game dynamics and extraction of event-specific team abilities, but also in predictions for the occurrence of events of interest, such as goals, corners or fouls in a specified interval of time.
翻译:我们开发了标记点过程的新组合, 将标记的霍克斯过程的特性完全集中在标记的空间上, 提供了为发生时间指定不同模式的自由。 通过分解标记和时间的联合分布, 从而可以单独指定标记的有条件分布, 以过滤过程和当前时间为条件。 我们开发了一个巴伊西亚框架, 用于从这个组合中推断和预测标记点过程的特性, 这些过程可以自然地容纳过程和点特定的共变信息, 以驱动交叉引用, 在模拟真实世界过程时提供广泛的灵活性和适用性。 框架在这里用于模拟组合足球的游戏中事件序列, 不仅导致对游戏动态和特定事件团队能力的提取先前未分化特性的推断, 而且还导致对特定时间段的目标、 角 或 污点 等利益事件的发生预测 。