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 oer 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 covariateadjusted 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.

Consonni, G., La Rocca, L., Peluso, S., Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection, <<SCANDINAVIAN JOURNAL OF STATISTICS>>, 2017; (44): 741-764. [doi:10.1111/sjos.12273] [http://hdl.handle.net/10807/97841]

Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection

Consonni, Guido;Peluso, Stefano
2017

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 oer 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 covariateadjusted 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.
Inglese
Consonni, G., La Rocca, L., Peluso, S., Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection, <<SCANDINAVIAN JOURNAL OF STATISTICS>>, 2017; (44): 741-764. [doi:10.1111/sjos.12273] [http://hdl.handle.net/10807/97841]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/97841
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