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Bayes Variable Selection in Semiparametric Linear Models

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  • Suprateek Kundu
  • David B. Dunson

Abstract

There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures of g -priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g -prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation can proceed via a straightforward stochastic search variable selection algorithm. In addition, Bayes' factor and variable selection consistency is shown to result under a class of proper priors on g even when the number of candidate predictors p is allowed to increase much faster than sample size n , while making sparsity assumptions on the true model size.

Suggested Citation

  • Suprateek Kundu & David B. Dunson, 2014. "Bayes Variable Selection in Semiparametric Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 437-447, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:437-447
    DOI: 10.1080/01621459.2014.881153
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    References listed on IDEAS

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    1. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    1. Nadja Klein & Michael Stanley Smith, 2021. "Bayesian variable selection for non‐Gaussian responses: a marginally calibrated copula approach," Biometrics, The International Biometric Society, vol. 77(3), pages 809-823, September.
    2. Subharup Guha & Rex Jung & David Dunson, 2022. "Predicting phenotypes from brain connection structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 639-668, June.
    3. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    4. Inkoo Lee & Debajyoti Sinha & Qing Mai & Xin Zhang & Dipankar Bandyopadhyay, 2023. "Bayesian regression analysis of skewed tensor responses," Biometrics, The International Biometric Society, vol. 79(3), pages 1814-1825, September.

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