A0368
Title: The G-Wishart weighted proposal algorithm: Efficient posterior computation for Gaussian graphical models
Authors: Willem van den Boom - National University of Singapore (Singapore) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Maria De Iorio - National University of Singapore (Singapore)
Abstract: Gaussian graphical models can capture complex dependency structures among variables. Bayesian inference is attractive for such models as it provides principled ways to incorporate prior information and quantify uncertainty through the posterior distribution. However, posterior computation under the conjugate G-Wishart prior distribution on the precision matrix is expensive for general non-decomposable graphs. Therefore a new Markov chain Monte Carlo (MCMC) method is proposed named the G-Wishart weighted proposal algorithm (WWA). WWA's distinctive features include delayed acceptance MCMC, Gibbs updates for the precision matrix and an informed proposal distribution on the graph space that enables embarrassingly parallel computations. Compared to existing approaches, WWA reduces the frequency of the relatively expensive sampling from the G-Wishart distribution. This results in faster MCMC convergence, improved MCMC mixing and reduced computing time. Numerical studies on simulated and real data show that WWA provides a more efficient tool for posterior inference than competing state-of-the-art MCMC algorithms.
