贝叶斯有限混合模型
Bayesian Finite Mixture Models
AI总结：
本文系统阐述贝叶斯有限混合模型在聚类中的应用，涵盖成分数已知与未知两种情况下的先验设定、MCMC估计、标签切换处理及后验推断，并通过多元高斯混合模型实例说明完整建模流程。
摘要：
有限混合模型是一类用于聚类和密度逼近的有用统计模型。在贝叶斯框架下，有限混合模型除了数据模型之外，还需要指定合适的先验分布。这些先验有助于避免虚假结果，并提供了一种有原则的方式来定义簇形状以及对特定聚类解的偏好。当混合成分数量固定时，可以使用带数据扩充的马尔可夫链蒙特卡洛（MCMC）采样获得通用的模型估计方案。后验分布允许以全面的方式评估不确定性，但针对特定成分的后验推断需要解决标签切换问题。本文聚焦于贝叶斯有限混合模型在聚类中的应用。我们首先讨论在假设成分数量已知的情况下模型的合适设定、估计和推断。随后继续解释当成分数量未知时拟合贝叶斯有限混合模型的合适策略。此外，通过一个拟合多元高斯分布有限混合模型的数据示例，说明了执行贝叶斯有限混合建模所需的所有步骤。针对该示例，分别在假设成分数量已知和未知的情况下，讨论了合适的先验设定、使用MCMC的估计以及后验推断。
英文摘要：
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors allow to avoid spurious results and provide a principled way to define cluster shapes and a preference for specific cluster solutions. A generic model estimation scheme for finite mixtures with a fixed number of components is available using Markov chain Monte Carlo (MCMC) sampling with data augmentation. The posterior allows to assess uncertainty in a comprehensive way, but component-specific posterior inference requires resolving the label switching issue. In this paper we focus on the application of Bayesian finite mixture models for clustering. We start with discussing suitable specification, estimation and inference of the model if the number of components is assumed to be known. We then continue to explain suitable strategies for fitting Bayesian finite mixture models when the number of components is not known. In addition, all steps required to perform Bayesian finite mixture modeling are illustrated on a data example where a finite mixture model of multivariate Gaussian distributions is fitted. Suitable prior specification, estimation using MCMC and posterior inference are discussed for this example assuming the number of components to be known as well as unknown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
