Carvalho, C. M.; Scott, J. G. Objective Bayesian model selection in Gaussian graphical models. (English) Zbl 1170.62020 Biometrika 96, No. 3, 497-512 (2009). Summary: This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart \(g\)-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple hypothesis testing. We demonstrate our methods on a variety of simulated examples, concluding with a real example analyzing covariation in mutual-fund returns. These studies reveal that the combined use of a multiplicity-correction prior on graphs and fractional Bayes factors for computing marginal likelihoods yields better performance than existing Bayesian methods. Cited in 44 Documents MSC: 62F15 Bayesian inference 05C90 Applications of graph theory 65C60 Computational problems in statistics (MSC2010) Keywords:Bayesian model selection; fractional Bayes factor; Gaussian graphical model; hyper-inverse Wishart distribution; multiple hypothesis testing PDFBibTeX XMLCite \textit{C. M. Carvalho} and \textit{J. G. Scott}, Biometrika 96, No. 3, 497--512 (2009; Zbl 1170.62020) Full Text: DOI Link