Post-Processed Posteriors for Banded Covariances

We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing the posterior consists two steps. In first step, samples are obtained from conjugate inverse-Wishart posterior, which does not satisfy any structural restrictions. second transformed to restriction through function. conceptually straightforward procedure makes its computation efficient can render interval estimators functionals matrices. show that it has nearly optimal minimax rates for covariances among all possible pairs priors functions. Additionally, we provide theorem on credible set under finite dimension assumption. prove expected coverage probability 100(1??)% highest density region is asymptotically 1?? with respect conventional distribution. It implies is, average, advantages demonstrated by simulation study real data analysis.