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Inference of global clusters from locally distributed data. (English) Zbl 1330.62255

Summary: 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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains
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