A Pivotal Allocation-Based Algorithm for Solving the Label-Switching Problem in Bayesian Mixture Models. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Li, Han; Fan, Xiaodan
• Is Part Of: Journal of computational and graphical statistics. Volume 25:Issue 1(2016)
• Page Start: 266
• Page End: 283
• Publication Date: 2016-01-02
• Subjects: Identifiability -- Label-switching problem -- Markov chain Monte Carlo; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2014.983643
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract : In Bayesian analysis of mixture models, the label-switching problem occurs as a result of the posterior distribution being invariant to any permutation of cluster indices under symmetric priors. To solve this problem, we propose a novel relabeling algorithm and its variants by investigating an approximate posterior distribution of the latent allocation variables instead of dealing with the component parameters directly. We demonstrate that our relabeling algorithm can be formulated in a rigorous framework based on information theory. Under some circumstances, it is shown to resemble the classical Kullback-Leibler relabeling algorithm and include the recently proposed equivalence classes representatives relabeling algorithm as a special case. Using simulation studies and real data examples, we illustrate the efficiency of our algorithm in dealing with various label-switching phenomena. Supplemental materials for this article are available online.