A Direct Sampler for G-Wishart Variates

TL;DR

This paper introduces a direct sampling method for G-Wishart distributions, enabling efficient Bayesian inference in Gaussian graphical models and facilitating new model selection algorithms.

Contribution

It presents the first direct sampler for G-Wishart variates, improving computational efficiency and enabling novel transdimensional model search techniques.

Findings

Successful implementation of the direct sampler

Development of the double reversible jump algorithm

Validation through two illustrative studies

Abstract

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.