Under mild conditions, it is shown the strong consistency of the Bayes estimator of the density. Moreover, the Bayes risk (for some common loss functions) of the Bayes estimator of the density (i.e. the posterior predictive density) reaches zero when the sample size goes to $\infty$. In passing, a similar result is obtained for the estimation of the sampling distribution.

翻译：在温和条件下,可以证明Bayes估计密度的强烈一致性,此外,Bayes估计密度的Bayes风险(对于某些常见损失功能而言)在样本大小达到$/infty美元时,Bayes估计密度(即后方预测密度)的风险(对于某些常见损失功能)达到零,顺便说一下,在估计抽样分布时得出了类似结果。