Dynamic Bayesian clustering of sport activities

The monitoring of sport activities through the use of smart–devices is assuming an increasing importance in several disciplines. In this context, data are collected as a sequence of activities, where each activity is represented by a partially–observed multivariate time series characterized by complex dependence structures. We propose a Bayesian matrix–variate dynamic mixture model for clustering trajectories of a large panel N of P –variate time series. The matrix state space formulation allows to consider for both longitudinal and cross sectional dependence, accounting also for missing values and other anomalies that characterize this kind of data. A fully conjugate approach is adopted, and the relative Gibbs sampler to sample from the full posterior distribution is available. Computational achievements can be obtained by performing Kalman recursionson a reduced form of the vectorized model, and simulating cluster allocations in one step, by using a MH within Gibbs algorithm. In the empirical application we analyze the running activities of one athlete.