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October 2015 Bayesian linear regression with sparse priors
Ismaël Castillo, Johannes Schmidt-Hieber, Aad van der Vaart
Ann. Statist. 43(5): 1986-2018 (October 2015). DOI: 10.1214/15-AOS1334

Abstract

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.

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Ismaël Castillo. Johannes Schmidt-Hieber. Aad van der Vaart. "Bayesian linear regression with sparse priors." Ann. Statist. 43 (5) 1986 - 2018, October 2015. https://doi.org/10.1214/15-AOS1334

Information

Received: 1 March 2014; Revised: 1 March 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 06502640
MathSciNet: MR3375874
Digital Object Identifier: 10.1214/15-AOS1334

Subjects:
Primary: 62G20
Secondary: 62G05

Keywords: Bayesian inference , Sparsity

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 5 • October 2015
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