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We develop a new family of marked point processes by focusing thecharacteristic properties of marked Hawkes processes exclusively to the spaceof marks, providing the freedom to specify a different model for the occurrencetimes. This is possible through the decomposition of the joint distribution ofmarks and times that allows to separately specify the conditional distributionof marks given the filtration of the process and the current time. We develop aBayesian framework for the inference and prediction from this family of markedpoint processes that can naturally accommodate process and point-specificcovariate information to drive cross-excitations, offering wide flexibility andapplicability in the modelling of real-world processes. The framework is usedhere for the modelling of in-game event sequences from association football,resulting not only in inferences about previously unquantified characteristicsof game dynamics and extraction of event-specific team abilities, but also inpredictions for the occurrence of events of interest, such as goals, corners orfouls in a specified interval of time.

Flexible marked spatio-temporal point processes with applications to event sequences from association football