  In this paper, we propose a scalable Bayesian method for sparse covariance
matrix estimation by incorporating a continuous shrinkage prior with a
screening procedure. In the first step of the procedure, the off-diagonal
elements with small correlations are screened based on their sample
correlations. In the second step, the posterior of the covariance with the
screened elements fixed at $0$ is computed with the beta-mixture prior. The
screened elements of the covariance significantly increase the efficiency of
the posterior computation. The simulation studies and real data applications
show that the proposed method can be used for the high-dimensional problem with
the `large p, small n'. In some examples in this paper, the proposed method can
be computed in a reasonable amount of time, while no other existing Bayesian
methods can be. The proposed method has also sound theoretical properties. The
screening procedure has the sure screening property and the selection
consistency, and the posterior has the optimal minimax or nearly minimax
convergence rate under the Frobeninus norm.
