Section: New Results

Label switching in mixtures

Participants : Christophe Biernacki, Vincent Vandewalle.

During the last fifteen years there has been an increasing interest for using Bayesian methods in mixtures models. However, one of the principal issues of these methods is the non-identifiability of components caused by symmetric prior (whatever be the kind of variables), which makes the Gibbs outputs useless for inference; this problem is known as label switching. We propose to condition the posterior distribution by a particular numbering, not on the parameter as it is usually done, but rather on a latent partition, for which the posterior distributions are not any more strictly invariant up to a renumbering of the partition [26] , [19] , [32] . The importance of this asymmetry depends on the choice of partition space cutting. The challenge we address is to choose a particular cutting which is justified and also easy to compute. The idea is to use some properties of the (unavailable) completed posterior distribution.