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Objective Bayesian model selection in Gaussian graphical models. (English) Zbl 1170.62020
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.

##### MSC:
 62F15 Bayesian inference 05C90 Applications of graph theory 65C60 Computational problems in statistics (MSC2010)
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