In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's Kullback--Leibler condition on the prior, the true distribution and most probability measures in the support of the prior are required to possess moments up to an order which is determined by the order of the Wasserstein metric. We further investigate convergence rates of the posterior distributions for which we need stronger moment conditions. The required tail conditions are sharp in the sense that the posterior distribution may be inconsistent or contract slowly to the true distribution without these conditions. Our study involves techniques that build on recent advances on Wasserstein convergence of empirical measures. We apply the results to density estimation with a Dirichlet process mixture prior and conduct a simulation study for further illustration.

翻译：在本文中,我们使用瓦塞尔斯坦标准来研究后天分配的无症状特性。 我们的第一个目标是为后天分配提供足够的条件。 除了众所周知的施瓦兹对前的库尔贝克-利贝尔条件之外,支持前天分配的真正分布和最可能的措施必须具备达到由瓦塞斯坦标准顺序决定的顺序所需的时间。 我们进一步调查后天分配的趋同率,我们需要更强大的时刻条件。 所需的尾矿条件是尖锐的,因为后天分配可能前后不一致,或者在不按这些条件进行真正分配方面缓慢地合同。 我们的研究涉及在瓦塞斯坦最近经验性措施趋同方面的进展基础上发展的技术。 我们用结果来进行密度估计,先用迪里赫特工艺混合,然后进行模拟研究,以便进一步说明。