Bayesian mixture models (in)consistency for the number of clusters
研究了贝叶斯非参数混合模型在聚类数量估计上的一致性，发现多种先验过程（如Gibbs型过程）在真实成分数有限时后验不一致，并讨论了扩展后处理算法实现一致估计的方法。
Abstract Bayesian nonparametric mixture models are common for modeling complex data. While these models are well‐suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of components is finite, for the Dirichlet process and Pitman–Yor process mixture models. We extend these results to additional Bayesian nonparametric priors such as Gibbs‐type processes and finite‐dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman–Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a postprocessing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.