A Direct Sampler for G-Wishart Variates

The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independence
of a Gaussian graphical model. Although the distribution has received considerable attention, posterior inference
has proven computationally challenging, in part owing 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.