Objective Bayes Covariate‐Adjusted Sparse Graphical Model Selection
提出一种客观贝叶斯方法，用于高斯多元回归模型中的协方差选择，可同时进行变量选择和图模型选择，尤其适用于遗传基因组学中响应变量数远大于样本量的场景。
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.