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Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling

机译：马尔可夫链蒙特卡罗方法和贝叶斯混合建模中的标签切换问题

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摘要

In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. While MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps underappreciated, problems associated with the MCMC analysis of mixtures. The problems are mainly caused by the nonidentifiability of the components under symmetric priors, which leads to so-called label switching in the MCMC output. This means that ergodic averages of component specific quantities will be identical and thus useless for inference. We review the solutions to the label switching problem, such as artificial identifiability constraints, relabelling algorithms and label invariant loss functions. We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior specification.
机译：在过去的十年中，对有限混合模型的贝叶斯分析的兴趣急剧增加。这主要是由于马尔可夫链蒙特卡罗（MCMC）方法的出现。尽管MCMC提供了一种方便的方法来从复杂的统计模型中进行推论，但是与混合物的MCMC分析相关的问题很多，甚至可能未被充分认识。问题主要是由于对称先验条件下组件的不可识别性引起的，这导致了MCMC输出中的所谓标签切换。这意味着各组分特定数量的遍历平均值将是相同的，因此无法进行推断。我们回顾了标签交换问题的解决方案，例如人为的可识别性约束，重新标记算法和标签不变损失函数。我们还将审查为混合模型建议的各种MCMC采样方案，并讨论对先前规格的后验敏感性。

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