## Bayesian Analysis

### A Two-Component $G$-Prior for Variable Selection

#### Abstract

We present a Bayesian variable selection method based on an extension of the Zellner’s $g$-prior in linear models. More specifically, we propose a two-component $G$-prior, wherein a tuning parameter, calibrated by use of pseudo-variables, is introduced to adjust the distance between the two components. We show that implementing the proposed prior in variable selection is more efficient than using the Zellner’s $g$-prior. Simulation results also indicate that models selected using the method with the two-component $G$-prior are generally more favorable with smaller losses compared to other methods considered in our work. The proposed method is further demonstrated using our motivating gene expression data from a lung disease study, and ozone data analyzed in earlier studies.

#### Article information

Source
Bayesian Anal., Volume 11, Number 2 (2016), 353-380.

Dates
First available in Project Euclid: 5 May 2015

https://projecteuclid.org/euclid.ba/1430830144

Digital Object Identifier
doi:10.1214/15-BA953

Mathematical Reviews number (MathSciNet)
MR3471994

Zentralblatt MATH identifier
1357.62249

#### Citation

Zhang, Hongmei; Huang, Xianzheng; Gan, Jianjun; Karmaus, Wilfried; Sabo-Attwood, Tara. A Two-Component $G$ -Prior for Variable Selection. Bayesian Anal. 11 (2016), no. 2, 353--380. doi:10.1214/15-BA953. https://projecteuclid.org/euclid.ba/1430830144

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