The generalized nested common atoms model

Bayesian hierarchical nonparametric models offer a convenient framework for modeling nested data, where observations are organized into groups. These priors jointly accommodate the dependence among groups and among observations within the same group in a flexible way. Several recent instances of such models have combined nested levels of Dirichlet processes and a common sequence of atoms, a formulation that allows for multi-layered partitions, i.e., a simultaneous clustering of observations and groups. However, using a common set of atoms can lead to a forced high prior correlation between the generated random measures. This characteristic can cause shortcomings in the clustering results and even biased density estimation. Extending the nested process with more general stick-breaking specifications for the weights alleviates these issues. Specifically, the proposed generalized Common Atoms Model enhances the flexibility of the dependence structure and improves density estimation. Three notable instances, particularly useful for practical applications, are discussed, and an efficient Gibbs sampler algorithm for this novel nested mixture model is developed. Finally, posterior results are validated with simulation studies and a real data application.