Bayesian Structural Learning and Estimation in Gaussian Graphical Models and Hierarchical Log-Linear Models

• Activity Number: 399
• Type: Invited
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Adrian Dobra*+
• Companies: University of Washington
• Keywords: Bayesian statistics ; Gaussian Graphical models ; Contingency tables ; Stochastic search

Abstract

We describe a novel stochastic search algorithm for rapidly identifying regions of high posterior probability in large spaces of candidate models. This approach relies on the existence of a method to accurately and efficiently approximate the marginal likelihood associated with a model when it cannot be computed in closed form. To this end, we develop a new Laplace approximation method to the normalizing constant of a G-Wishart distribution associated with a Gaussian graphical model. We propose a similar method for computing the marginal likelihood of a hierarchical log-linear model based on the Diaconis-Ylvisaker conjugate prior for log-linear parameters. We show the efficiency of our methodology with respect to Markov chain Monte Carlo techniques and with other stochastic search algorithms proposed in the literature.