Group for Research in Decision Analysis

# A Stopping Rule for MCMC Clustering

## Vahid Partovi Nia

When a Bayesian model is formulated for clustering, often Markov chain Monte Carlo (MCMC) method is applied to sample allocations. Therefore a measure of convergence defined on the allocation space, a finite state space, is needed. Such a stopping rule can also be used to quantify efficiency of a chain. A Pearson-like goodness of fit statistic is introduced for Bayesian models with analytically tractable marginal posteriors. The asymptotic distribution of the statistic is derived under equilibrium providing a statistical significance test. Application of the proposed method is demonstrated on MCMC clustering of high-dimensional-low-sample-size metabolite data.