A Metropolis-Hastings based method for sampling from the G-Wishart distribution in Gaussian graphical models

Abstract

In Gaussian graphical models, the conjugate prior for the precision matrix K is called G-Wishart distribution, W_G(δ,D). In this paper we propose a new sampling method for the W_G(δ,D) based on the Metropolis Hastings algorithm and we show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing with a computationally inexpensive approach for model selection.