Interpretation and inference in mixture models: Simple MCMC works
Computational Statistics & Data Analysis
Bayesian finite mixtures with an unknown number of components: The allocation sampler
Statistics and Computing
Model based labeling for mixture models
Statistics and Computing
Maximum likelihood estimation of Gaussian mixture models using stochastic search
Pattern Recognition
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The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called `relabelling' strategies exist with the goal to `undo' the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Existing deterministic relabelling algorithms rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow for estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing deterministic relabelling algorithms. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.