In many applications, a finite mixture is a natural model, but it can be
difficult to choose an appropriate number of components. To circumvent this
choice, investigators are increasingly turning to Dirichlet process mixtures
(DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these
models may be well-suited for Bayesian density estimation, many investigators
are using them for inferences about the number of components, by considering
the posterior on the number of components represented in the observed data. We
show that this posterior is not consistent --- that is, on data from a finite
mixture, it does not concentrate at the true number of components. This result
applies to a large class of nonparametric mixtures, including DPMs and PYMs,
over a wide variety of families of component distributions, including
essentially all discrete families, as well as continuous exponential families
satisfying mild regularity conditions (such as multivariate Gaussians).

本文研究了有限混合模型的贝叶斯密度估计与数目成分推断中，使用狄利克雷过程混合模型（DPMs）和 Pitman-Yor 过程混合模型（PYMs）等非参数混合模型的后验分布并不一致，特别适用于大多数分布族，包括离散族以及满足柔性正则条件的连续指数族（如多元高斯分布）。