Abstract: A new procedure of learning in Gaussian graphical models is proposed under the assumption that samples are possibly dependent. This assumption, which is pragmatically applied in various areas of multivariate analysis ranging from bioinformatics to finance, makes standard Gaussian graphical models (GGMs) unsuitable. We demonstrate that the advantage of modeling dependence among samples is that the true discovery rate and positive predictive value are improved substantially than if standard GGMs are applied and the dependence among samples is ignored. The new method, called matrix-variate Gaussian graphical models (MGGMs), involves simultaneously modeling variable and sample dependencies with the matrix-normal distribution. The computation is carried out using a Markov chain Monte Carlo (MCMC) sampling scheme for graphical model determination and parameter estimation. Simulation studies and two real-world examples in biology and finance further illustrate the benefits of the new models.

Key words: Gaussian graphical models, Hyper-inverse Wishart distributions, Mutual fund evaluation, Network

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