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We consider the Bayesian mixture of finite mixtures (MFMs) and Dirichletprocess mixture (DPM) models for clustering. Recent asymptotic theory hasestablished that DPMs overestimate the number of clusters for large samples andthat estimators from both classes of models are inconsistent for the number ofclusters under misspecification, but the implications for finite sampleanalyses are unclear. The final reported estimate after fitting these models isoften a single representative clustering obtained using an MCMC summarisationtechnique, but it is unknown how well such a summary estimates the number ofclusters. Here we investigate these practical considerations throughsimulations and an application to gene expression data, and find that (i) DPMsoverestimate the number of clusters even in finite samples, but only to alimited degree that may be correctable using appropriate summaries, and (ii)misspecification can lead to considerable overestimation of the number ofclusters in both DPMs and MFMs, but results are nevertheless often stillinterpretable. We provide recommendations on MCMC summarisation and suggestthat although the more appealing asymptotic properties of MFMs provide strongmotivation to prefer them, results obtained using MFMs and DPMs are often verysimilar in practice.

Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?