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.

The pre-print of the paper can be accessed here.

 Santhosh Narayanan⁴, Ioannis Kosmidis¹ and Petros Dellaportas^2,3
 
1Department of Statistics, University of Warwick, Gibbet Hill Road, Coventry, CV4
7AL, UK
2Department of Statistical Science, University College London, Gower St., London,
WC1E 6BT, UK
3Department of Statistics, Athens University of Economics and Business, 76 Patission
Str., Athens, 10434, Greece
4The Alan Turing Institute, 96 Euston Road, London, England, NW1 2DB, UK
 

Jotham Gaudoin for RSS Statistics in Sport Section and Judith Shorten on behalf of the RSS Discussion Meetings Committee