  A nonparanormal graphical model is a semiparametric generalization of a
Gaussian graphical model for continuous variables in which it is assumed that
the variables follow a Gaussian graphical model only after some unknown smooth
monotone transformations. We consider a Bayesian approach to inference in a
nonparanormal graphical model in which we put priors on the unknown
transformations through a random series based on B-splines. We use a regression
formulation to construct the likelihood through the Cholesky decomposition on
the underlying precision matrix of the transformed variables and put shrinkage
priors on the regression coefficients. We apply a plug-in variational Bayesian
algorithm for learning the sparse precision matrix and compare the performance
to a posterior Gibbs sampling scheme in a simulation study. We finally apply
the proposed methods to a real data set. KEYWORDS:
