CliPS -- How to identify cluster distributions in Bayesian mixture models

We propose the CliPS procedure when fitting Bayesian mixture models in the context of model-based clustering to identify the cluster distributions while simultaneously assessing the suitability of a cluster solution and validating the cluster structure. The procedure relies on the point process representation of a mixture model and is based on the assumption that a suitable cluster solution requires the clusters to be distinguishable with respect to a low-dimensional functional of the component-specific parameters of the mixture. CliPS maps the component-specific MCMC draws to the point process representation and identifies clusters there, exploiting that, while data distributions usually overlap, the posterior of these functionals are more and more separated for increasing sample size. We outline the procedure and illustrate its use on several model-based clustering examples.