论文标题
关于贝叶斯的密度和采样分布的估计：后验预测分布作为贝叶斯估计器
On Bayesian Estimation of Densities and Sampling Distributions: the Posterior Predictive Distribution as the Bayes Estimator
论文作者
论文摘要
在本文中给出了两个未出色的贝叶斯估计问题的最佳结果：平方总变化函数的采样分布的估计以及$ l^1 $平方损耗函数的密度估计。后验预测分布为这些问题提供了解决方案。提出了一些示例来说明它。还解决了分布函数的贝叶斯估计问题。证明了密度估计器的一致性。
Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss function. The posterior predictive distribution provides the solution to these problems. Some examples are presented to illustrate it. The Bayesian estimation problem of a distribution function is also addressed. Consistency of the estimator of the density is proved.
