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arXiv · 1406.7718

Empirical Bayes posterior concentration in sparse high-dimensional linear models

Ryan Martin·Raymond Mess·Stephen G. Walker
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Abstract

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.

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Ryan Martin, Raymond Mess, Stephen G. Walker. 2018-12-05. Empirical Bayes posterior concentration in sparse high-dimensional linear models. https://doi.org/10.3150/15-bej797

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