Posterior graph selection and estimation consistency for high-dimensional Bayesian DAG models (Q1731759)

A quite challenging problem of modern statistics is covariance estimation and selection for high-dimensional multivariate datasets. A flexible and general class of the Gaussian directed acyclic graph (DAG) priors with multiple shape parameters is considered. Under mild regularity assumptions, consistency and posterior convergence order is established when the number of variables $p$ is allowed to grow at an appropriate subexponential rate with the sample size $n$.