Objective Bayes Covariate‐Adjusted Sparse Graphical Model Selection. (29th March 2017)

• Record Type: Journal Article
• Authors: Consonni, Guido; La Rocca, Luca; Peluso, Stefano
• Is Part Of: Scandinavian journal of statistics. Volume 44:Number 3(2017:Sep.)
• Page Start: 741
• Page End: 764
• Publication Date: 2017-03-29
• Subjects: Bayesian model selection -- covariance selection -- decomposable graphical model -- directed acyclic graphical model -- fractional Bayes factor -- Gaussian graphical model -- Gaussian multivariate regression -- marginal likelihood -- model sparsity -- variable selection; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12273
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: We present an objective Bayes method for covariance selection in Gaussian multivariate regression models having a sparse regression and covariance structure, the latter being Markov with respect to a directed acyclic graph (DAG). Our procedure can be easily complemented with a variable selection step, so that variable and graphical model selection can be performed jointly. In this way, we offer a solution to a problem of growing importance especially in the area of genetical genomics (eQTL analysis). The input of our method is a single default prior, essentially involving no subjective elicitation, while its output is a closed form marginal likelihood for every covariate‐adjusted DAG model, which is constant over each class of Markov equivalent DAGs; our procedure thus naturally encompasses covariate‐adjusted decomposable graphical models. In realistic experimental studies, our method is highly competitive, especially when the number of responses is large relative to the sample size.