A Convergence Diagnostic for Bayesian Clustering

Many convergence diagnostics for Markov chain Monte Carlo (MCMC) are well-calibrated to continuous and ordinal target distributions. However, Bayesian clustering requires convergence on an immense nominal state space: that of all possible clusterings of a given dataset. We propose a Hotelling-type convergence diagnostic for MCMC on such spaces. Leveraging knowledge of the unnormalized posterior distribution, our diagnostic assesses not only whether the MCMC has converged, but also whether convergence is to the correct result. This is illustrated with a Bayesian clustering analysis of genetic mutants of the flowering plant Arabidopsis thaliana.