Bayesian structured variable selection in linear regression models

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• 作者：Min Wang (1)
  Xiaoqian Sun (2)
  Tao Lu (3)
  
  1. Department of Mathematical Sciences ; Michigan Technological University ; Houghton ; MI ; 49931 ; USA
  2. Department of Mathematical Sciences ; Clemson University ; Clemson ; SC ; 29634 ; USA
  3. Department of Epidemiology and Biostatistics ; State University of New York ; Albany ; NY ; 12144 ; USA
  
• 关键词：Interactions ; Generalized singular $$g$$ g ; prior ; Beta ; prime prior ; Posterior probability ; Gibbs sampler ; Consistency
• 刊名：Computational Statistics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：30
• 期：1
• 页码：205-229
• 全文大小：399 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Probability and Statistics in Computer Science
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1613-9658

文摘

In this paper we consider the Bayesian approach to the problem of variable selection in normal linear regression models with related predictors. We adopt a generalized singular \(g\) -prior distribution for the unknown model parameters and the beta-prime prior for the scaling factor \(g\) , which results in a closed-form expression of the marginal posterior distribution without integral representation. A special prior on the model space is then advocated to reflect and maintain the hierarchical or structural relationships among predictors. It is shown that under some nominal assumptions, the proposed approach is consistent in terms of model selection and prediction. Simulation studies show that our proposed approach has a good performance for structured variable selection in linear regression models. Finally, a real-data example is analyzed for illustrative purposes.