Post-processed posteriors for sparse covariances
提出一种两步法后处理后验分布，先获取共轭逆Wishart后验样本，再通过广义阈值函数施加稀疏结构，在高维设置下达到最优极小化收敛速度，并应用于近似因子模型的稀疏特质协方差估计。
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 a generalized thresholding function. This non-traditional Bayesian procedure is justified by showing that the post-processed posterior attains the optimal minimax rates under the spectral norm loss in high-dimensional settings. We also propose the post-processed posterior for contaminated data and apply it to the estimation of the sparse idiosyncratic covariance of the approximate factor model. The advantages of our method are demonstrated via a simulation study and a real data analysis with S&P 500 data.