Label Switching in Mixture Models

• Activity Number: 386
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Eric Loken*+
• Companies: Pennsylvania State University
• Keywords: mixture models ; Bayesian inference ; label switching

Abstract

A well-known identification problem in estimating mixture models is that the observed data likelihood is invariant to permutations of the group labels. In Bayesian estimation, label switching during posterior simulation will distort posterior summaries. A proposal to address mode-switching is offered. If one or more cases are "pre-classified," that is, if the group membership is assumed to be known, label switching can be dramatically reduced. In a mixture of two groups, assuming that a case belongs to group 1 can be considered as simply defining the labeling. The modification is easy to implement in an EM algorithm to maximize the likelihood, and also in MCMC simulation of the posterior distribution. It can be shown that pre-classifying modifies the likelihood by eliminating the nuisance mode and leaving the mode of interest almost perfectly intact. MCMC simulations with a latent class model and with a mixture of two exponentials show that the technique works well and compares favorably with other strategies. The extension of the technique to mixtures with three or more components will be explored.