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An exact sampler for fully Baysian elastic net

Author

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  • Hai-Bin Wang

    (Xiamen University)

  • Jian Wang

    (Xiamen University)

Abstract

The elastic net plays an important role in regularization regressions. We develop a new hybrid Gibbs sampler for the fully Bayesian elastic net, in which we make use of the exchange algorithm to draw the penalized parameter from its full conditional posterior with an intractable normalizing constant. A great advantage of the proposed sampler is that it is exact and/or time-saving. Moreover, we consider a novel algorithm to sample the standard deviation of the model error from its full conditional that includes the auxiliary vector no longer. We also incorporate a generalised move step in our approach to improve the convergence further. The performance of the proposed method is demonstrated by four simulated examples and the prostate cancer data, and compared with that of the existing methods.

Suggested Citation

  • Hai-Bin Wang & Jian Wang, 2023. "An exact sampler for fully Baysian elastic net," Computational Statistics, Springer, vol. 38(4), pages 1721-1734, December.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-022-01275-8
    DOI: 10.1007/s00180-022-01275-8
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    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.
    4. van Dyk, David A. & Park, Taeyoung, 2008. "Partially Collapsed Gibbs Samplers: Theory and Methods," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 790-796, June.
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