论文标题
使用来自平均值和方差未知的正常观察的信息，用于卡方模型的贝叶斯预测密度估计
Bayesian Predictive Density Estimation for a Chi-squared Model Using Information from a Normal Observation with Unknown Mean and Variance
论文作者
论文摘要
在本文中，我们考虑了根据观察到另一个卡方变量和kullback-leibler脱离的正常变量估算卡方变量的密度函数的问题。我们假设这些变量具有一个常见的未知量表参数，并且正常变量的平均值也未知。我们比较了两个贝叶斯预测密度的风险功能：一个关于层次收缩的先验，另一个是基于非信息的先验。分层贝叶斯的预测密度取决于正常变量，而基于非信息先验的贝叶斯预测密度则不取决于正常变量。获得了足够的条件，以使前者占主导地位。通过模拟比较这些预测密度。
In this paper, we consider the problem of estimating the density function of a Chi-squared variable on the basis of observations of another Chi-squared variable and a normal variable under the Kullback-Leibler divergence. We assume that these variables have a common unknown scale parameter and that the mean of the normal variable is also unknown. We compare the risk functions of two Bayesian predictive densities: one with respect to a hierarchical shrinkage prior and the other based on a noninformative prior. The hierarchical Bayesian predictive density depends on the normal variable while the Bayesian predictive density based on the noninformative prior does not. Sufficient conditions for the former to dominate the latter are obtained. These predictive densities are compared by simulation.
