  We consider the problem of analyzing the heterogeneity of clustering
distributions for multiple groups of observed data, each of which is indexed by
a covariate value, and inferring global clusters arising from observations
aggregated over the covariate domain. We propose a novel Bayesian nonparametric
method reposing on the formalism of spatial modeling and a nested hierarchy of
Dirichlet processes. We provide an analysis of the model properties, relating
and contrasting the notions of local and global clusters. We also provide an
efficient inference algorithm, and demonstrate the utility of our method in
several data examples, including the problem of object tracking and a global
clustering analysis of functional data where the functional identity
information is not available.
