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 $(1-\alpha)100\%$ highest posterior density region of the post-processed posterior is asymptotically $1-\alpha$ 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.

翻译：我们认为带宽共变矩阵的贝氏推论是贝氏变异矩阵的推论,并提议一个后处理后后后后附体。后后后处理由两步组成。第一步,从不满足任何结构性限制的反Wishart后附体中采集后附体样本。第二步,后后加后后附体样本通过后处理功能转换以满足结构性限制。后处理后后后后后后后后后后后后后附体的简单程序使其计算效率高,并可以使共变矩阵功能的间隙估计器。我们显示,后后后加后后后后附和后处理功能中所有可能配对的带宽变体中,后加体样本几乎具有最佳的最小变异率。此外,我们证明,后处理后后后后后后后后后后后后后后加后后后后后后后加后后后后后附体最高的后附体密度区域的预期覆盖概率值概率,对于传统的后加后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后分配的后加分析是一套可靠数据分析的一套数据优势分析的一套可靠数据优势。