Finite mixture model for multiple sample data

In this paper, we propose a Bayesian nonparametric level-dependent mixture model for clustering. To achieve this, we employ a vector of species sampling models with shared atoms and level-specific weights. This results in multiple random probability measures with a common support, which we use to perform both inter-level and within-level clustering of the data. This approach enables us to take into account both heterogeneity and common patterns shared across levels in our clustering analysis. Specifically, we study the properties of the group-dependent clustering structure induced by our hierarchical mixture model. We develop both a marginal and a conditional Gibbs sampler to perform Bayesian inference. We evaluate the model’s ability to recover the original clustering of the data and assess its goodness of fit through simulated data.