The paper by Matthew Stephens addresses the "label switching" problem in Bayesian analysis of finite mixture models, where the likelihood remains unchanged under permutations of the mixture components, leading to symmetric and multimodal posterior distributions. This symmetry can make parameter estimation and clustering difficult. Stephens critiques the common practice of using artificial identifiability constraints to remove label switching, arguing that this approach often fails to provide satisfactory solutions. Instead, he proposes a class of *relabelling algorithms* that aim to minimize the posterior expected loss under a suitable loss function. These algorithms are motivated by a decision-theoretic framework, where the goal is to choose actions that minimize the expected loss. Stephens provides a detailed description of one such algorithm and demonstrates its effectiveness through examples, showing that it successfully addresses label switching in both simple and complex scenarios. The paper also discusses the computational aspects and extensions of the algorithms, including an online version that reduces storage requirements. Overall, the relabelling algorithms offer a more robust and flexible solution to the label switching problem compared to traditional methods.The paper by Matthew Stephens addresses the "label switching" problem in Bayesian analysis of finite mixture models, where the likelihood remains unchanged under permutations of the mixture components, leading to symmetric and multimodal posterior distributions. This symmetry can make parameter estimation and clustering difficult. Stephens critiques the common practice of using artificial identifiability constraints to remove label switching, arguing that this approach often fails to provide satisfactory solutions. Instead, he proposes a class of *relabelling algorithms* that aim to minimize the posterior expected loss under a suitable loss function. These algorithms are motivated by a decision-theoretic framework, where the goal is to choose actions that minimize the expected loss. Stephens provides a detailed description of one such algorithm and demonstrates its effectiveness through examples, showing that it successfully addresses label switching in both simple and complex scenarios. The paper also discusses the computational aspects and extensions of the algorithms, including an online version that reduces storage requirements. Overall, the relabelling algorithms offer a more robust and flexible solution to the label switching problem compared to traditional methods.