ABSTRACT We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet process). The asymptotic results for the posterior distribution of the proposed models are derived, including posterior consistency and posterior contraction rate in the context of nonparametric density estimation. More importantly, we show that compared to the independent prior on the component centers, the repulsive prior introduces additional shrinkage effect on the tail probability of the posterior number of components, which serves as a measurement of the model complexity. In addition, a generalized urn model that allows a random number of components and correlated component centers is developed based on the exchangeable partition distribution, which gives rise to the corresponding blocked-collapsed Gibbs sampler for posterior inference. We evaluate the performance and demonstrate the advantages of the proposed methodology through extensive simulation studies and real data analysis. Supplementary materials for this article are available online.

中文翻译：

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贝叶斯排斥高斯混合模型

摘要 我们开发了一类通用的贝叶斯排斥高斯混合模型，这些模型鼓励分离良好的集群，旨在减少由位置的独立先验（例如狄利克雷过程）产生的潜在冗余分量。推导出所提出模型的后验分布的渐近结果，包括非参数密度估计背景下的后验一致性和后验收缩率。更重要的是，我们表明，与组件中心的独立先验相比，排斥性先验对后验数量的组件的尾部概率引入了额外的收缩效应，作为模型复杂性的度量。此外，基于可交换分区分布开发了一个允许随机数量的组件和相关组件中心的广义 urn 模型，这产生了用于后验推理的相应块折叠 Gibbs 采样器。我们通过广泛的模拟研究和真实数据分析来评估性能并证明所提出方法的优势。本文的补充材料可在线获取。