  We propose the Plaid Atoms Model (PAM), a novel Bayesian nonparametric model
for grouped data. Founded on an idea of `atom skipping', PAM is part of a
well-established category of models that generate dependent random
distributions and clusters across multiple groups. Atom skipping referrs to
stochastically assigning 0 weights to atoms in an infinite mixture. Deploying
atom skipping across groups, PAM produces a dependent clustering pattern with
overlapping and non-overlapping clusters across groups. As a result,
interpretable posterior inference is possible such as reporting the posterior
probability of a cluster being exclusive to a single group or shared among a
subset of 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 with comparison to
existing models.
