ABSTRACT We propose an approach for fitting multi‐cluster data using copula‐based Dirichlet process mixture models (DPM). Unlike conventional finite mixture models, our framework uses Sklar's theorem to accommodate heterogeneous marginal distributions and complex inter‐variable dependencies. We adopt a slice‐sampling MCMC scheme to enable full Bayesian inference, which makes the posterior distribution on the number of clusters and the cluster‐specific copula parameters simultaneously available. Simulation studies show that this DPM‐copula approach can accurately capture and recover heavy‐tailed or skewed clusters, while the Gaussian mixture model cannot. We apply our method to real NBA player‐level advanced statistics from the 2021–2024 seasons, demonstrating how the model discovers distinct subgroups that exhibit different correlation structures and marginal shapes. These insights show the advantages of a flexible, copula‐based approach for multi‐cluster data analysis in sports analytics and beyond.
Liu et al. (Tue,) studied this question.