Is label switching problem a problem?

In many models, the likelihood is invariant under parameters permutation. In such situations, using an invariant prior like independent prior, will lead to an invariant and multimodal posterior. In practice, the very famous case is the Bayesian mixture modeling. A problem of parameters (non) identifiability will appear. This is also called label switching. For example all the posterior means will appear. This is also called label switching. For example all the posterior means will have the same value and hence no individual inference can be done from MCMC output. In this work, we will show the problems linked to the label switching mainly in the case of mixture. We will discuss two kind of solution. The first deals with the output itself without considering the associated algorithm. The second suggests different amelioration of the sampling method.

Keywords:

Label Switching , (non) Identifiability , Mixture , MCMC Sampling , Multimodality.