  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 a 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 the 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.
