Posterior convergence rates for high-dimensional precision matrix estimation using G-Wishart priors

We study the posterior convergence behaviour of a precision matrix corresponding to a Gaussian graphical model in the high-dimensional set-up under sparsity assumptions. Recent works include studying posterior convergence rates of precision matrices assuming an approximate banding structure, and extension of such result to arbitrary decomposable graphical models using a transformation to Cholesky factor of the precision matrices. In this paper, we study the same for the wider class of arbitrary decomposable graphical models under similar sparsity assumptions using a G-Wishart prior, but without the complications of using a Cholesky factor, and arrive at identical posterior convergence rates. Copyright (C) 2017 John Wiley & Sons, Ltd.