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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 semiparametric 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 by putting priors on the unknown transformations through a random series based on B-splines. A truncated normal prior leads to partial conjugacy in the model and is useful for posterior simulation using Gibbs sampling. On the underlying precision matrix of the transformed variables, we consider a spike-and-slab prior and use an efficient posterior Gibbs sampling scheme. We present a posterior consistency result on the underlying transformation and the precision matrix. We study the numerical performance of the proposed method and apply the method on a real dataset.
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