Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection

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 ste...

Full description

Saved in:
Bibliographic Details
Published in:Scandinavian journal of statistics 2017-09, Vol.44 (3), p.741-764
Main Authors: CONSONNI, GUIDO, LA ROCCA, LUCA, PELUSO, STEFANO
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian model selection
Covariance
covariance selection
decomposable graphical model
directed acyclic graphical model
Economic models
Exact solutions
fractional Bayes factor
Gaussian graphical model
Gaussian multivariate regression
International
marginal likelihood
Markov analysis
Markov chains
model sparsity
Regression analysis
Statistical analysis
Studies
variable selection
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12273