@article{mulgrave_ghosal_2023, title={Bayesian analysis of nonparanormal graphical models using rank-likelihood}, volume={222}, ISSN={["1873-1171"]}, DOI={10.1016/j.jspi.2022.06.006}, abstractNote={Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality assumption may be restrictive in many settings. 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 for 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 on its Cholesky decomposition and use a posterior Gibbs sampling scheme. We present a posterior consistency result for the precision matrix based on the rank-based likelihood. We study the numerical performance of the proposed method through a simulation study and apply it on a real dataset.}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Mulgrave, Jami J. and Ghosal, Subhashis}, year={2023}, month={Jan}, pages={195–208} }