Bayesian Repulsive Gaussian Mixture Model
提出一类贝叶斯排斥高斯混合模型，通过鼓励聚类分离来减少冗余成分，推导了后验一致性和收缩率，并开发了广义瓮模型和吉布斯采样算法。
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.