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.
Original language | English |
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Pages (from-to) | 741-764 |
Number of pages | 24 |
Journal | Scandinavian Journal of Statistics |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Bayesian Model Selection