A Bayesian Approach for Partial Gaussian Graphical Models With Sparsity

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable deal with single-output as well multiple-output linear regressions, in small or high dimension, enforcing either no sparsity, group sparsity even sparse-group for a bi-level selection through correlations (direct links) between predictors and responses, thanks spike-and-slab priors corresponding each setting. Adaptative global shrinkages are also incorporated the modeling of direct links. An existing result model consistency is reformulated stick our sparse group-sparse settings, providing theoretical guarantee under some technical assumptions. Gibbs samplers developed simulation study shows efficiency models which give very competitive results, especially terms support recovery. To conclude, real dataset investigated.