Bayesian Estimation of Large Precision Matrix Based on Cholesky Decomposition

Abstract

In this paper, we consider the estimation of a high dimensional precision matrix of Gaussian graphical model. Based on the re-parameterized likelihood, we obtain the full conditional distribution of all parameters in Cholesky factor. Furthermore, by imposing the prior information, we obtain the shrinkage Bayesian estimator of large precision matrix, and establish the asymptotic distribution of all parameters in the Cholesky factor. At last, we demonstrate our method through the simulation study and an application to telephone call center data.