Bayesian inference for nondecomposable graphical Gaussian models

In this paper we propose a method to calculate the posterior probability of a nondecomposable graphical Gaussian model. Our proposal is based on a new device to sample from Wishart distributions, conditional on the graphical constraints. As a result, our methodology allows Bayesian model selection within the whole class of graphical Gaussian models, including nondecomposable ones. 1 INTRODUCTION Let G be a conditional independence graph, describing the association structure of a vector of random variables, say X. A graphical model is a family of probability distributions P G which is Markov over G. In particular, when all the random variables in X are continuous, a graphical Gaussian model is obtained by assuming P G = N(¯; \Sigma G ), with \Sigma G positive definite and such that P G is Markov over G. For an introduction to graphical models, see for instance Lauritzen (1996) or Whittaker (1990). Typically the association structure of X is uncertain and, thus, has to be inferred from..