Abstract: We consider problems involving functional data where we have a collection of functions, each viewed as a process realization, e.g., a random curve or surface. For a particular process realization, we assume that the observation at a given location can be allocated to separate groups via a random allocation process, which we name the Dirichlet labeling process. We investigate properties of this process and its use as a prior in a mixture model. We develop exact and approximate representations for the labeling process, analyze the global and local clustering behavior, clarify model identifiability and posterior consistency, and develop efficient inference methods for models using such priors. Performance is demonstrated with synthetic data examples, a public-health application, and an image segmentation task.
Key words and phrases: Clustering, Dirichlet process mixtures, Gaussian processes, Gibbs posterior, hybrid Dirichlet process, variational Bayes.