  We propose a new empirical Bayes approach for inference in the $p \gg n$
normal linear model. The novelty is the use of data in the prior in two ways,
for centering and regularization. Under suitable sparsity assumptions, we
establish a variety of concentration rate results for the empirical Bayes
posterior distribution, relevant for both estimation and model selection.
Computation is straightforward and fast, and simulation results demonstrate the
strong finite-sample performance of the empirical Bayes model selection
procedure.
