Hierarchical Dirichlet process mixture models for local and global clustering in longitudinal studies.

The problem of performance modelling in sport has received considerable attention in the literature devoted to statistics and sports analytics. Indeed, the modelling of teams' and players' performance data is essential in order to perform complex analyses that involve predictions or decisions. The applied motivation for this work arises precisely in sports analytics: the interest of this study is to cluster together athletes having a similar average performance within a season, and then link clusters across different seasons in order to learn similarities or differences in performance. This can be accomplished by assuming that the observations of each athlete are random perturbations of an underlying individual step function and considering its levels as season-specific random intercepts. Indeed, using a hierarchical Dirichlet process as a nonparametric prior allows to generate ties in the latent random intercepts both across seasons and athletes, thus inducing a clustering of the observations. The study is conducted on a real world data set consisting of data recorded during professional shot put competitions held throughout 19 seasons.