  The G-Wishart distribution is the conjugate prior for precision matrices that
encode the conditional independencies of a Gaussian graphical model. While the
distribution has received considerable attention, posterior inference has
proven computationally challenging, in part due to the lack of a direct
sampler. In this note, we rectify this situation. The existence of a direct
sampler offers a host of new possibilities for the use of G-Wishart variates.
We discuss one such development by outlining a new transdimensional model
search algorithm--which we term double reversible jump--that leverages this
sampler to avoid normalizing constant calculation when comparing graphical
models. We conclude with two short studies meant to investigate our algorithm's
validity.
