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Efficient sampling of Gaussian graphical models using conditional Bayes factors
Author(s) -
Hinne Max,
Lenkoski Alex,
Heskes Tom,
Gerven Marcel
Publication year - 2014
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.66
Subject(s) - wishart distribution , graphical model , conjugate prior , gaussian , computer science , algorithm , bayes' theorem , posterior probability , hyperparameter , artificial intelligence , bayesian probability , mathematics , pattern recognition (psychology) , machine learning , physics , multivariate statistics , quantum mechanics
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G ‐Wishart distribution, has a doubly intractable partition function. Recent developments provide a direct way to sample from the G ‐Wishart distribution, which allows for more efficient algorithms for model selection than previously possible. Still, estimating Gaussian graphical models with more than a handful of variables remains a nearly infeasible task. Here, we propose two novel algorithms that use the direct sampler to more efficiently approximate the posterior distribution of the Gaussian graphical model. The first algorithm uses conditional Bayes factors to compare models in a Metropolis–Hastings framework. The second algorithm is based on a continuous time Markov process. We show that both algorithms are substantially faster than state‐of‐the‐art alternatives. Finally, we show how the algorithms may be used to simultaneously estimate both structural and functional connectivity between subcortical brain regions using resting‐state functional magnetic resonance imaging. Copyright © 2014 John Wiley & Sons, Ltd.