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Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective

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  • P. Richard Hahn
  • Carlos M. Carvalho

Abstract

Selecting a subset of variables for linear models remains an active area of research. This article reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

Suggested Citation

  • P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:509:p:435-448
    DOI: 10.1080/01621459.2014.993077
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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. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
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    5. 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.
    6. Fouskakis, Dimitris & Draper, David, 2008. "Comparing Stochastic Optimization Methods for Variable Selection in Binary Outcome Prediction, With Application to Health Policy," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1367-1381.
    7. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    8. J. E. Griffin & P. J. Brown, 2012. "Structuring shrinkage: some correlated priors for regression," Biometrika, Biometrika Trust, vol. 99(2), pages 481-487.
    9. Nicholas G. Polson & James G. Scott, 2012. "Local shrinkage rules, Lévy processes and regularized regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 287-311, March.
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    Citations

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    Cited by:

    1. David Kohns & Tibor Szendrei, 2021. "Decoupling Shrinkage and Selection for the Bayesian Quantile Regression," Papers 2107.08498, arXiv.org.
    2. Niko Hauzenberger & Florian Huber & Luca Onorante, 2021. "Combining shrinkage and sparsity in conjugate vector autoregressive models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 304-327, April.
    3. Niko Hauzenberger & Florian Huber & Gary Koop, "undated". "Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods," Working Papers 2305, University of Strathclyde Business School, Department of Economics.
    4. Daniel R. Kowal, 2023. "Subset selection for linear mixed models," Biometrics, The International Biometric Society, vol. 79(3), pages 1853-1867, September.
    5. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    6. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    7. Byron Botha & Rulof Burger & Kevin Kotzé & Neil Rankin & Daan Steenkamp, 2023. "Big data forecasting of South African inflation," Empirical Economics, Springer, vol. 65(1), pages 149-188, July.
    8. Qifan Song & Guang Cheng, 2020. "Bayesian Fusion Estimation via t Shrinkage," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-385, August.
    9. Li, Hanning & Pati, Debdeep, 2017. "Variable selection using shrinkage priors," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 107-119.
    10. David Puelz & Carlos M. Carvalho & P. Richard Hahn, 2015. "Optimal ETF Selection for Passive Investing," Papers 1510.03385, arXiv.org, revised Nov 2015.
    11. Rodney A. Sparapani & Brent R. Logan & Martin J. Maiers & Purushottam W. Laud & Robert E. McCulloch, 2023. "Nonparametric failure time: Time‐to‐event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures," Biometrics, The International Biometric Society, vol. 79(4), pages 3023-3037, December.
    12. Robert B. Gramacy, 2020. "Discussion," International Statistical Review, International Statistical Institute, vol. 88(2), pages 326-329, August.
    13. Xueying Tang & Xiaofan Xu & Malay Ghosh & Prasenjit Ghosh, 2018. "Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage Priors," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 215-246, August.
    14. David Puelz & P. Richard Hahn & Carlos M. Carvalho, 2020. "Portfolio selection for individual passive investing," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(1), pages 124-142, January.
    15. Kohns, David & Potjagailo, Galina, 2023. "Flexible Bayesian MIDAS: time‑variation, group‑shrinkage and sparsity," Bank of England working papers 1025, Bank of England.
    16. Kirsner, Daniel & Sansó, Bruno, 2020. "Multi-scale shotgun stochastic search for large spatial datasets," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).

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