Statistical modeling in presence of hierarchical data is a crucial task in
Bayesian statistics. The Hierarchical Dirichlet Process (HDP) represents the
utmost tool to handle data organized in groups through mixture modeling.
Although the HDP is mathematically tractable, its computational cost is
typically demanding, and its analytical complexity represents a barrier for
practitioners. The present paper conceives a mixture model based on a novel
family of Bayesian priors designed for multilevel data and obtained by
normalizing a finite point process. A full distribution theory for this new
family and the induced clustering is developed, including tractable expressions
for marginal, posterior and predictive distributions. Efficient marginal and
conditional Gibbs samplers are designed for providing posterior inference. The
proposed mixture model overcomes the HDP in terms of analytical feasibility,
clustering discovery, and computational time. The motivating application comes
from the analysis of shot put data, which contains performance measurements of
athletes across different seasons. In this setting, the proposed model is
exploited to induce clustering of the observations across seasons and athletes.
By linking clusters across seasons, similarities and differences in athlete's
performances are identified