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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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    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.
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    Cited by:

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    2. 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.
    3. David Kohns & Tibor Szendrei, 2021. "Decoupling Shrinkage and Selection for the Bayesian Quantile Regression," Papers 2107.08498, arXiv.org.
    4. 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.
    5. Hauzenberger Niko & Huber Florian & Koop Gary, 2024. "Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 201-225, April.
    6. Li, Hanning & Pati, Debdeep, 2017. "Variable selection using shrinkage priors," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 107-119.
    7. David Puelz & Carlos M. Carvalho & P. Richard Hahn, 2015. "Optimal ETF Selection for Passive Investing," Papers 1510.03385, arXiv.org, revised Nov 2015.
    8. Jan Prüser & Florian Huber, 2024. "Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 269-291, March.
    9. Li, Fanqun & Zhao, Mingtao & Zhang, Kongsheng, 2024. "Bayesian adaptive Lasso estimation of large graphical model based on modified Cholesky decomposition," Statistics & Probability Letters, Elsevier, vol. 206(C).
    10. Daniel R. Kowal, 2023. "Subset selection for linear mixed models," Biometrics, The International Biometric Society, vol. 79(3), pages 1853-1867, September.
    11. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    12. 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.
    13. Robert B. Gramacy, 2020. "Discussion," International Statistical Review, International Statistical Institute, vol. 88(2), pages 326-329, August.
    14. 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.
    15. 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.
    16. 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.
    17. Kohns, David & Potjagailo, Galina, 2023. "Flexible Bayesian MIDAS: time‑variation, group‑shrinkage and sparsity," Bank of England working papers 1025, Bank of England.
    18. 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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