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March 2020 High-Dimensional Posterior Consistency for Hierarchical Non-Local Priors in Regression
Xuan Cao, Kshitij Khare, Malay Ghosh
Bayesian Anal. 15(1): 241-262 (March 2020). DOI: 10.1214/19-BA1154


The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an important tuning parameter which reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. Current approaches treat the scale parameter as given, and suggest choices based on prior coverage/asymptotic considerations. In this paper, we consider the fully Bayesian approach introduced in (Wu, 2016) with the pMOM non-local prior and an appropriate Inverse-Gamma prior on the tuning parameter to analyze the underlying theoretical property. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where p is allowed to increase at a polynomial rate with n or even at a sub-exponential rate with n. Through simulation studies, we demonstrate that our model selection procedure can outperform other Bayesian methods which treat the scale parameter as given, and commonly used penalized likelihood methods, in a range of simulation settings.


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Xuan Cao. Kshitij Khare. Malay Ghosh. "High-Dimensional Posterior Consistency for Hierarchical Non-Local Priors in Regression." Bayesian Anal. 15 (1) 241 - 262, March 2020.


Published: March 2020
First available in Project Euclid: 19 April 2019

zbMATH: 1437.62253
MathSciNet: MR4050884
Digital Object Identifier: 10.1214/19-BA1154


Vol.15 • No. 1 • March 2020
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