Modal Clustering in Univariate, Conjugate Dirichlet Process Mixture Models

The Dirichlet Process mixture (DPM) model is a popular nonparametric Bayesian tool for modeling unknown distributions through mixtures of components. Integrating out the latent location variables in a DPM model leads to a product partition model. This paper describes a modefinding algorithm which quickly finds either the maximizer of the partition posterior or the maximizer of the partition likelihood in a class of product partition models. Sufficient conditions when the algorithm can be used are given and these conditions are shown to be satisfied in several univariate, conjugate DPM models. Clustering observations based on a modal partition is a modelbased clustering procedure which, prior to this work, could only be approximated. The proposed procedure is demonstrated in a microarray dataset of expression levels of more than 10,000 genes.