Sub-optimality of some continuous shrinkage priors
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.
Keywords
Cite
@article{arxiv.1605.05671,
title = {Sub-optimality of some continuous shrinkage priors},
author = {Anirban Bhattacharya and David B. Dunson and Debdeep Pati and Natesh S. Pillai},
journal= {arXiv preprint arXiv:1605.05671},
year = {2016}
}
Comments
Some of the results were announced in this earlier paper arXiv:1212.6088. To appear in Stochastic Processes and Applications, special issue in memoriam Prof. Evarist Gine