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Dirichlet-Laplace priors for optimal shrinkage.

Publication ,  Journal Article
Bhattacharya, A; Pati, D; Pillai, NS; Dunson, DB
Published in: Journal of the American Statistical Association
December 2015

Penalized regression methods, such as L1 regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians, facilitating computation. In contrast to the frequentist literature, little is known about the properties of such priors and the convergence and concentration of the corresponding posterior distribution. In this article, we propose a new class of Dirichlet-Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation. Finite sample performance of Dirichlet-Laplace priors relative to alternatives is assessed in simulated and real data examples.

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Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

December 2015

Volume

110

Issue

512

Start / End Page

1479 / 1490

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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Bhattacharya, A., Pati, D., Pillai, N. S., & Dunson, D. B. (2015). Dirichlet-Laplace priors for optimal shrinkage. Journal of the American Statistical Association, 110(512), 1479–1490. https://doi.org/10.1080/01621459.2014.960967
Bhattacharya, Anirban, Debdeep Pati, Natesh S. Pillai, and David B. Dunson. “Dirichlet-Laplace priors for optimal shrinkage.Journal of the American Statistical Association 110, no. 512 (December 2015): 1479–90. https://doi.org/10.1080/01621459.2014.960967.
Bhattacharya A, Pati D, Pillai NS, Dunson DB. Dirichlet-Laplace priors for optimal shrinkage. Journal of the American Statistical Association. 2015 Dec;110(512):1479–90.
Bhattacharya, Anirban, et al. “Dirichlet-Laplace priors for optimal shrinkage.Journal of the American Statistical Association, vol. 110, no. 512, Dec. 2015, pp. 1479–90. Epmc, doi:10.1080/01621459.2014.960967.
Bhattacharya A, Pati D, Pillai NS, Dunson DB. Dirichlet-Laplace priors for optimal shrinkage. Journal of the American Statistical Association. 2015 Dec;110(512):1479–1490.

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

December 2015

Volume

110

Issue

512

Start / End Page

1479 / 1490

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics