Section: New Results

Label switching in Bayesian mixture model estimation

Participants : Christophe Biernacki, Benjamin Guedj, Vincent Vandewalle.

In the case of mixtures of distributions, it is well-known that the Bayesian posterior distribution is invariant to label switching, it means invariant to any renumbering of components. Consequences are important, typically leading to unuseful estimates like the posterior mean. Many attempts exist to solve this problem but it is advocated in this work that such a quest should be unfruitful since it is a direct consequence of the label non-identifiability of mixtures themselves. The present work proposes an original way to manage the label switching problem based on the Gibbs algorithm dynamic. The basic idea is to control the label switching probability along Gibbs iterations, controlled by both the sample size and the component overlap. An early version of this work has been presented as an invited talk to the international workshop [28].