The label switching problem in mixture models

Mixture models are fascinating objects in that, while based on elementary distributions, they offer a much wider range of modeling possibilities than their components. They also need both highly complex computational challenges and delicate inferential derivations. In Bayesian framework these kinds of models do not admit an analytical solution and one should content him/her by an approximative solution. In this work, we introduce definition of identifiability in statistical model. We focus on definition of identifiability of mixtures of models from Bayesian point of view. This issue is called label-switching problem in Bayesian literatures. We will study a method to identify the mixtures parameter by using MCMC output.