A Class of Dependent Random Distributions Based on Atom Skipping
Dehua Bi, Yuan Ji · Bayesian Analysis · 2026
We propose a Bayesian nonparametric model for grouped data called the Shared Atoms Model (SAM). SAM generates dependent random discrete distributions through “atom skipping,” where a mixture component may have zero weight in some groups. This allows the model to represent unique, shared, and common clusters, and to estimate the extent of overlap across groups. As a result, interpretable posterior inference is feasible, such as reporting the posterior probability of a unique cluster exclusive to a single group or a shared cluster belonging to some but not all groups. We discuss the theoretical properties of the proposed and related models. Minor extensions of the proposed model for multivariate or count data are presented. Simulation studies and applications using real-world datasets illustrate the performance of the new models in comparison with existing models. The code is publicly available at https://github.com/edwardbi/SharedAtomsModel.