Mixture Models

5Label switching for mixture models

DOI: 10.1201/9781003038511-5

Label switching has long been a challenging problem for both Bayesian and Frequentist finite mixtures. It arises due to the invariance of the mixture likelihood to the relabeling of the mixture components. For Bayesian mixtures, if the prior is symmetric for the component parameters, the posterior distribution is invariant under the relabeling of the mixture components. Without solving the label switching, the ergodic averages (based on posterior or bootstrap samples) of component-specific quantities will be identical, becoming useless for inference relating to individual components, such as the component-specific parameters, predictive component densities, and marginal classification ...