Acceleration of the stochastic search variable selection via componentwise Gibbs sampling

Hengzhen Huang, Shuangshuang Zhou, Min-Qian Liu () and Zong-Feng Qi
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Hengzhen Huang: Guangxi Normal University
Shuangshuang Zhou: Nankai University
Min-Qian Liu: Nankai University
Zong-Feng Qi: The State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System (CEMEE)

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 3, No 3, 289-308

Abstract: Abstract The stochastic search variable selection proposed by George and McCulloch (J Am Stat Assoc 88:881–889, 1993) is one of the most popular variable selection methods for linear regression models. Many efforts have been proposed in the literature to improve its computational efficiency. However, most of these efforts change its original Bayesian formulation, thus the comparisons are not fair. This work focuses on how to improve the computational efficiency of the stochastic search variable selection, but remains its original Bayesian formulation unchanged. The improvement is achieved by developing a new Gibbs sampling scheme different from that of George and McCulloch (J Am Stat Assoc 88:881–889, 1993). A remarkable feature of the proposed Gibbs sampling scheme is that, it samples the regression coefficients from their posterior distributions in a componentwise manner, so that the expensive computation of the inverse of the information matrix, which is involved in the algorithm of George and McCulloch (J Am Stat Assoc 88:881–889, 1993), can be avoided. Moreover, since the original Bayesian formulation remains unchanged, the stochastic search variable selection using the proposed Gibbs sampling scheme shall be as efficient as that of George and McCulloch (J Am Stat Assoc 88:881–889, 1993) in terms of assigning large probabilities to those promising models. Some numerical results support these findings.

Keywords: Bayesian variable selection; Gibbs sampler; Linear regression; Stochastic search variable selection; Supersaturated design; Primary 62J05; Secondary 62K15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00184-016-0604-x

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