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Sub-optimality of some continuous shrinkage priors

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  • Bhattacharya, Anirban
  • Dunson, David B.
  • Pati, Debdeep
  • Pillai, Natesh S.

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, have 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.

Suggested Citation

  • Bhattacharya, Anirban & Dunson, David B. & Pati, Debdeep & Pillai, Natesh S., 2016. "Sub-optimality of some continuous shrinkage priors," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3828-3842.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:12:p:3828-3842
    DOI: 10.1016/j.spa.2016.08.007
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
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