论文标题
后处理的后代协方差
Post-Processed Posteriors for Banded Covariances
论文作者
论文摘要
我们认为贝叶斯对带的协方差矩阵的推断，并提出后处理后部。后验的后处理包括两个步骤。在第一步中，后样品是从不满足任何结构限制的偶联逆偏式后置。在第二步中，将后样品转换为通过后处理函数满足结构限制。后处理后验的概念上的直接过程使其计算有效，并可以渲染协方差矩阵功能的间隔估计器。我们表明，在所有可能的先验和后加工功能中，带带的协方差率几乎具有最佳的最小值速率。此外，我们证明，相对于常规后验分布，后处理后的$（1-α）100 \％最高后密度区域的预期覆盖率是渐近的$ 1-α$。这意味着后处理后的最高后密度区域平均是一组可信的常规后部。通过模拟研究和真实的数据分析证明了后处理后验的优势。
We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior which does not satisfy any structural restrictions. In the second step, the posterior samples are transformed to satisfy the structural restriction through a post-processing function. The conceptually straightforward procedure of the post-processed posterior makes its computation efficient and can render interval estimators of functionals of covariance matrices. We show that it has nearly optimal minimax rates for banded covariances among all possible pairs of priors and post-processing functions. Furthermore, we prove that the expected coverage probability of the $(1-α)100\%$ highest posterior density region of the post-processed posterior is asymptotically $1-α$ with respect to a conventional posterior distribution. It implies that the highest posterior density region of the post-processed posterior is, on average, a credible set of a conventional posterior. The advantages of the post-processed posterior are demonstrated by a simulation study and a real data analysis.
