Bayesian Inference in Nonparanormal Graphical Models

Abstract

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.

References in corpus (15)

• High-dimensional graphs and variable selection with the Lasso
• Optimal predictive model selection
• Extended Bayesian Information Criteria for Gaussian Graphical Models
• Sparse permutation invariant covariance estimation
• Copula Gaussian graphical models and their application to modeling functional disability data
• Bayesian Structure Learning in Sparse Gaussian Graphical Models
• BDgraph: An R Package for Bayesian Structure Learning in Graphical Models
• Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
• Wishart distributions for decomposable graphs
• Scaling It Up: Stochastic Search Structure Learning in Graphical Models
• Sparse Inverse Covariance Selection via Alternating Linearization Methods
• Posterior convergence rates for estimating large precision matrices using graphical models
• Bayesian Gaussian Copula Graphical Modeling for Dupuytren Disease
• Bayesian inference with rescaled Gaussian process priors
• Bayesian optimal adaptive estimation using a sieve prior

Cited by in corpus (1)

• Monte Carlo inference for semiparametric Bayesian regression