论文标题
基于扩展模型和收缩贝叶斯方法的多元正常模型的预测密度
Predictive densities for multivariate normal models based on extended models and shrinkage Bayes methods
论文作者
论文摘要
我们研究了具有未知平均向量和已知协方差矩阵的多元正常模型的预测密度。基于收缩率的贝叶斯预测密度通常具有复杂的表示，尽管它们在各种问题中有效。我们将具有平均向量和协方差矩阵的扩展正常模型视为参数，并采用属于包括原始正常模型的扩展模型的预测密度。在扩展模型中，我们采用有关后贝叶斯风险最佳的预测密度。基于超谐波收缩先验的提议的预测密度显示出基于损失函数在基于kullback-leibler差异下的均匀先验的贝叶斯预测密度主导的预测密度。我们的方法提供了经验贝叶斯方法的替代方法，该方法广泛用于构建可拖动的预测密度。
We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are effective in various problems. We consider extended normal models with mean vectors and covariance matrices as parameters, and adopt predictive densities that belong to the extended models including the original normal model. We adopt predictive densities that are optimal with respect to the posterior Bayes risk in the extended models. The proposed predictive density based on a superharmonic shrinkage prior is shown to dominate the Bayesian predictive density based on the uniform prior under a loss function based on the Kullback-Leibler divergence. Our method provides an alternative to the empirical Bayes method, which is widely used to construct tractable predictive densities.
