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Bayesian group selection in logistic regression with application to MRI data analysis

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  • Kyoungjae Lee
  • Xuan Cao

Abstract

We consider Bayesian logistic regression models with group‐structured covariates. In high‐dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high‐dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state‐of‐the‐art methods in various settings. We further apply our method to a magnetic resonance imaging data set for predicting Parkinson's disease and show its benefits over other contenders.

Suggested Citation

  • Kyoungjae Lee & Xuan Cao, 2021. "Bayesian group selection in logistic regression with application to MRI data analysis," Biometrics, The International Biometric Society, vol. 77(2), pages 391-400, June.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:2:p:391-400
    DOI: 10.1111/biom.13290
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    References listed on IDEAS

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    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Sean M. O'Brien & David B. Dunson, 2004. "Bayesian Multivariate Logistic Regression," Biometrics, The International Biometric Society, vol. 60(3), pages 739-746, September.
    3. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
    4. Naveen N. Narisetty & Juan Shen & Xuming He, 2019. "Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1205-1217, July.
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    Cited by:

    1. Ouyang, Jiarong & Cao, Xuan, 2024. "Consistent skinny Gibbs in probit regression," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).

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