  We consider Bayesian inference of sparse covariance matrices and propose a
post-processed posterior. This method consists of two steps. In the first step,
posterior samples are obtained from the conjugate inverse-Wishart posterior
without considering the sparse structural assumption. The posterior samples are
transformed in the second step to satisfy the sparse structural assumption
through the hard-thresholding function. This non-traditional Bayesian procedure
is justified by showing that the post-processed posterior attains the optimal
minimax rates. We also investigate the application of the post-processed
posterior to the estimation of the global minimum variance portfolio. We show
that the post-processed posterior for the global minimum variance portfolio
also attains the optimal minimax rate under the sparse covariance assumption.
The advantages of the post-processed posterior for the global minimum variance
portfolio are demonstrated by a simulation study and a real data analysis with
S&P 400 data.
