Grün, Bettina; Leisch, Friedrich
Dealing with Label Switching in Mixture Models Under Genuine Multimodality.
In: Journal of Multivariate Analysis
The fitting of finite mixture models is an ill-defined estimation problem as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label
switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed and their application is demonstrated on artificial and real-world data.