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Abstract:
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Gaussian graphical models, where it is assumed that the variables of interest jointly follow multivariate normal distributions with sparse precision matrices, have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a nonparametric generalization of a Gaussian graphical model for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformation. We consider a Bayesian approach in the nonparanormal graphical model using a rank likelihood which remains invariant under monotone transformations, thereby avoiding the need to put a prior on the transformation functions. On the underlying precision matrix of the transformed variables, we consider a horseshoe prior using a Bayesian regression approach and use an efficient posterior Gibbs sampling scheme. We study the numerical performance of the proposed method through a simulation study and apply it on a real dataset.
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