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arXiv · 1605.05671

Sub-optimality of some continuous shrinkage priors

Anirban Bhattacharya·David B. Dunson·Debdeep Pati·Natesh S. Pillai
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Abstract

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and non-sparse posterior summaries under standard loss functions, has motivated an amazing variety of continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians. Interestingly, we demonstrate that many commonly used shrinkage priors, including the Bayesian Lasso, do not have adequate posterior concentration in high-dimensional settings.

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Anirban Bhattacharya, David B. Dunson, Debdeep Pati, Natesh S. Pillai. 2016-05-18. Sub-optimality of some continuous shrinkage priors. https://arxiv.org/abs/1605.05671

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