Salon 2
Bayesian inference in nonparanormal graphical models (303253)
Subhashis Ghoshal, North Carolina State University*Jami Jackson Mulgrave, North Carolina State University
Keywords: Bayesian, graphical models, nonparanormal, B-splines, prior
Gaussian graphical models, where it is assumed that the variables of interest jointly follow multivariate normal distributions with sparse precision matrices, have been extensively used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a non-parametric 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 where the coefficients are ordered to induce monotonicity. It is seen that a suitably truncated normal prior leads to partial conjugacy in the model and hence is useful for posterior simulation within a Hamiltonian Monte Carlo sampling setting. In addition, we prove the consistency of the estimators using hypothesis testing. We demonstrate the method in a simulation study and with a real dataset.