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We begin by reviewing some probabilistic results about the Dirichlet Processand its close relatives, focussing on their implications for statisticalmodelling and analysis. We then introduce a class of simple mixture models inwhich clusters are of different `colours', with statistical characteristicsthat are constant within colours, but different between colours. Thus clusteridentities are exchangeable only within colours. The basic form of our model isa variant on the familiar Dirichlet process, and we find that much of thestandard modelling and computational machinery associated with the Dirichletprocess may be readily adapted to our generalisation. The methodology isillustrated with an application to the partially-parametric clustering of geneexpression profiles.

Colouring and breaking sticks: random distributions and heterogeneous clustering