Relabelling in Bayesian mixture models by pivotal units

TL;DR

This paper introduces a simple, low-cost relabeling method for Bayesian mixture models to address label switching issues in MCMC sampling, especially when component ordering is ambiguous.

Contribution

It proposes a practical relabeling procedure based on pivotal units, offering an easy-to-implement solution for complex posterior distributions in finite mixture models.

Findings

Effective in reducing label switching in mixture models

Low computational overhead compared to existing methods

Applicable when component ordering is not straightforward

Abstract

In this paper a simple procedure 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 very 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.