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Abstract:
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One of the most fundamental problems for Bayesian mixture model analysis is label switching, which occurs due to the non-identifiability of the mixture components under symmetric priors. The widely used and easiest way to solve the label switching is to use an explicit parameter constraint so that only one permutation can satisfy it. Here, we propose a new labeling method we call PM(ECM), which assigns the labels based on the modes one converges to using the ECM algorithm. Due to the ascending property of the ECM algorithm, the PM(ECM) labeling method automatically matches the "ideal" labels in the highest posterior density (HPD) credible region. Hence the PM(ECM) creates a natural and intuitive partition of the parameter space into labeled regions. Using a real data set and a Monte Carlo simulation study, we demonstrate how effectively our new labeling method works.
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