Posterior convergence rates for high‐dimensional precision matrix estimation usingG‐Wishart priors

Abstract

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 aG‐Wishart prior, but without the complications of using a Cholesky factor, and arrive at identical posterior convergence rates. Copyright © 2017 John Wiley & Sons, Ltd.