In Gaussian graphical models, the conjugate prior for the precision matrix K is called G-Wishart distribution, WG(δ,D). In this paper we propose a new sampling method for the WG(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.
"A Metropolis-Hastings based method for sampling from the G-Wishart distribution in Gaussian graphical models." Electron. J. Statist. 5 18 - 30, 2011. https://doi.org/10.1214/11-EJS594