  Gaussian graphical models 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 for continuous variables where it is assumed that the variables
follow a Gaussian graphical model only after some unknown smooth monotone
transformations on each of them. 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 where the coefficients are ordered
to induce monotonicity. 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
use the Bayesian Information Criterion to choose the hyperparameters for the
spike-and-slab prior. We present a posterior consistency result on the
underlying transformation and the precision matrix. We study the numerical
performance of the proposed method through an extensive simulation study and
finally apply the proposed method on a real data set.
