Open Access
June 2020 A Loss-Based Prior for Variable Selection in Linear Regression Methods
Cristiano Villa, Jeong Eun Lee
Bayesian Anal. 15(2): 533-558 (June 2020). DOI: 10.1214/19-BA1162


In this work we propose a novel model prior for variable selection in linear regression. The idea is to determine the prior mass by considering the worth of each of the regression models, given the number of possible covariates under consideration. The worth of a model consists of the information loss and the loss due to model complexity. While the information loss is determined objectively, the loss expression due to model complexity is flexible and, the penalty on model size can be even customized to include some prior knowledge. Some versions of the loss-based prior are proposed and compared empirically. Through simulation studies and real data analyses, we compare the proposed prior to the Scott and Berger prior, for noninformative scenarios, and with the Beta-Binomial prior, for informative scenarios.


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Cristiano Villa. Jeong Eun Lee. "A Loss-Based Prior for Variable Selection in Linear Regression Methods." Bayesian Anal. 15 (2) 533 - 558, June 2020.


Published: June 2020
First available in Project Euclid: 14 June 2019

MathSciNet: MR4078724
Digital Object Identifier: 10.1214/19-BA1162

Keywords: Bayesian variable selection , Linear regression , loss functions , objective priors

Vol.15 • No. 2 • June 2020
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