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Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis

Author

Listed:
  • Aijun Yang

    (Nanjing Forestry University
    Southeast University)

  • Xuejun Jiang

    (South University of Science and Technology of China)

  • Lianjie Shu

    (University of Macau)

  • Jinguan Lin

    (Southeast University)

Abstract

The main challenge in working with gene expression microarrays is that the sample size is small compared to the large number of variables (genes). In many studies, the main focus is on finding a small subset of the genes, which are the most important ones for differentiating between different types of cancer, for simpler and cheaper diagnostic arrays. In this paper, a sparse Bayesian variable selection method in probit model is proposed for gene selection and classification. We assign a sparse prior for regression parameters and perform variable selection by indexing the covariates of the model with a binary vector. The correlation prior for the binary vector assigned in this paper is able to distinguish models with the same size. The performance of the proposed method is demonstrated with one simulated data and two well known real data sets, and the results show that our method is comparable with other existing methods in variable selection and classification.

Suggested Citation

  • Aijun Yang & Xuejun Jiang & Lianjie Shu & Jinguan Lin, 2017. "Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis," Computational Statistics, Springer, vol. 32(1), pages 127-143, March.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0665-3
    DOI: 10.1007/s00180-016-0665-3
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    References listed on IDEAS

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    1. Gupta, Mayetri & Ibrahim, Joseph G., 2007. "Variable Selection in Regression Mixture Modeling for the Discovery of Gene Regulatory Networks," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 867-880, September.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    4. Chakraborty, Sounak, 2009. "Bayesian binary kernel probit model for microarray based cancer classification and gene selection," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4198-4209, October.
    5. Yuan, Ming & Lin, Yi, 2005. "Efficient Empirical Bayes Variable Selection and Estimation in Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1215-1225, December.
    6. Baragatti, M. & Pommeret, D., 2012. "A study of variable selection using g-prior distribution with ridge parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1920-1934.
    7. Naijun Sha & Marina Vannucci & Mahlet G. Tadesse & Philip J. Brown & Ilaria Dragoni & Nick Davies & Tracy C. Roberts & Andrea Contestabile & Mike Salmon & Chris Buckley & Francesco Falciani, 2004. "Bayesian Variable Selection in Multinomial Probit Models to Identify Molecular Signatures of Disease Stage," Biometrics, The International Biometric Society, vol. 60(3), pages 812-819, September.
    8. Li, Fan & Zhang, Nancy R., 2010. "Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces With Applications in Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1202-1214.
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