MCMC and the Label Switching Problem in Bayesian Mixture Modelling 1 Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modelling
MCMC and the Label Switching Problem in Bayesian Mixture Modelling 1 Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modelling
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MCMC 和贝叶斯混合建模中的标签切换问题 1 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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发表时间：
2004
期刊：
影响因子：
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通讯作者：
D. Stephens
中科院分区：
文献类型：
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作者：
A. Jasra;C. Holmes;D. Stephens
在过去十年中，人们对有限混合模型的贝叶斯分析的兴趣急剧增加。这主要是因为马尔可夫链蒙特卡罗（MCMC）方法的出现。虽然 MCMC 提供了一种从复杂的统计模型中进行推断的便捷方法，但仍然存在许多与混合物 MCMC 分析相关的问题，这些问题可能未被充分认识到。这些问题主要是由对称先验下组件的不可识别性引起的，这导致了 MCMC 输出中所谓的标签交换。这意味着组分特定量的遍历平均值将是相同的，因此对于推理是无用的。我们回顾了标签切换问题的解决方案，例如人工可识别性约束（例如 Diebolt & Robert (1994)）、重新标签算法（Stephens 1997a）和标签不变损失函数（Celeux、Hurn & Robert 2000）。我们还回顾了为混合模型建议的各种 MCMC 抽样方案，并讨论了对先验规范的后验敏感性。
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. Whilst MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps under appreciated, 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 will mean 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 (e.g. Diebolt & Robert (1994)), relabelling algorithms (Stephens 1997a) and label invariant loss functions (Celeux, Hurn & Robert 2000). We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior specification.