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Title: A Bayesian approach to coloured graphical Gaussian models Authors:  Qiong Li - York University (Canada)
Helene Massam - York University (Canada) [presenting]
Xin Xin Gao - York University (Canada)
Abstract: The focus is on graphical Gaussian models $N_p(0, \Sigma)$ Markov with respect to an undirected graph $G$, with additional symmetry constraints on the entries of the precision matrix $K=\Sigma^{-1}$. We give an overview of recent results for estimation and model selection in this class of models: the Diaconis-Ylvisaker conjugate prior, called the coloured $G$-Wishart, a Bayesian estimate of $\Sigma$ and $K$, its asymptotic behaviour when $p$ is fixed and the number $n$ of sample points tends to infinity or, when both $p$ and $n$ tend to infinity, and also an efficient double reversible jump Markov chain Monte Carlo algorithm for estimating Bayes factors in model selection.