Annals of Statistics
- Ann. Statist.
- Volume 42, Number 2 (2014), 789-817.
Bayesian variable selection with shrinking and diffusing priors
Naveen Naidu Narisetty and Xuming He
Abstract
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the $L_{0}$ penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives.
Article information
Source
Ann. Statist., Volume 42, Number 2 (2014), 789-817.
Dates
First available in Project Euclid: 20 May 2014
Permanent link to this document
https://projecteuclid.org/euclid.aos/1400592178
Digital Object Identifier
doi:10.1214/14-AOS1207
Mathematical Reviews number (MathSciNet)
MR3210987
Zentralblatt MATH identifier
1302.62158
Subjects
Primary: 62J05: Linear regression 62F12: Asymptotic properties of estimators 62F15: Bayesian inference
Keywords
Bayes factor hierarchical model high dimensional data shrinkage variable selection
Citation
Narisetty, Naveen Naidu; He, Xuming. Bayesian variable selection with shrinking and diffusing priors. Ann. Statist. 42 (2014), no. 2, 789--817. doi:10.1214/14-AOS1207. https://projecteuclid.org/euclid.aos/1400592178
Supplemental materials
- Supplementary material: Supplement to “Bayesian variable selection with shrinking and diffusing priors”. This supplement contains the proofs of Theorems 4.1, 4.2 and Lemma 4.2.Digital Object Identifier: doi:10.1214/14-AOS1207SUPP
