An artificial allocations based solution to the label switching problem
in Bayesian analysis of mixtures of distributions
P. Papastamoulis and G. Iliopoulos
The Label Switching is a well-known problem occuring in MCMC outputs in Bayesian mixture modelling. In this paper we propose a formal solution to this problem by considering the space of the artificial allocation variables. We show that there exist certain subsets of the allocation space leading to a class of nonsymmetric distributions that have the same support with the symmetric posterior distribution and can reproduce it by simply permutating the labels. Moreover, we select one of these distributions as a solution to the label switching problem using the simple matching distance between the artificial allocation variables. The proposed algorithm can be used in any mixture model and its computational cost depends on the length of the simulated chain but not on the parameter space dimension.
Real and simulated data examples are provided in both univariate and multivariate settings. Supplemental material for this article is available online.
Key words and phrases: Mixtures of distributions; Markov chain Monte Carlo; label switching problem; data augmentation; Pivotal Reordering algorithm; genuine multimodality