Relabelling in Bayesian mixture models by pivotal units

A simple procedure based on relabelling to deal with label switching when exploring complex posterior distributions by MCMC algorithms is proposed. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and low computational burden. A possible area where it proves to be useful is when deriving a sample for the posterior distribution arising from finite mixture models when no simple or rational ordering between the components is available.