IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v103y2016i4p955-969..html
   My bibliography  Save this article

Default Bayesian analysis with global-local shrinkage priors

Author

Listed:
  • Anindya Bhadra
  • Jyotishka Datta
  • Nicholas G. Polson
  • Brandon Willard

Abstract

We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we show that the horseshoe priors, originally designed to handle sparsity, are regularly varying and thus are appropriate for default Bayesian analysis. To illustrate our methodology, we discuss four problems of noninformative priors that have been shown to be highly informative for nonlinear functions. In each case, we show that global-local horseshoe priors perform as required. Global-local shrinkage priors can separate a low-dimensional signal from high-dimensional noise even for nonlinear functions.

Suggested Citation

  • Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon Willard, 2016. "Default Bayesian analysis with global-local shrinkage priors," Biometrika, Biometrika Trust, vol. 103(4), pages 955-969.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:955-969.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asw041
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jose Ailton Alencar Andrade & Anthony O'Hagan, 2011. "Bayesian Robustness Modelling of Location and Scale Parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 691-711, December.
    2. Nadarajah, Saralees, 2009. "PDFs and Dual PDFs," The American Statistician, American Statistical Association, vol. 63(1), pages 45-48.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michele Costola & Matteo Iacopini & Casper Wichers, 2023. "Bayesian SAR model with stochastic volatility and multiple time-varying weights," Papers 2310.17473, arXiv.org.
    2. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon T. Willard, 2020. "Global-Local Mixtures: A Unifying Framework," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 426-447, August.
    3. Adam N. Smith & Jim E. Griffin, 2023. "Shrinkage priors for high-dimensional demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 21(1), pages 95-146, March.
    4. Iacopini, Matteo & Poon, Aubrey & Rossini, Luca & Zhu, Dan, 2023. "Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    5. Anindya Bhadra & Jyotishka Datta & Yunfan Li & Nicholas Polson, 2020. "Horseshoe Regularisation for Machine Learning in Complex and Deep Models," International Statistical Review, International Statistical Institute, vol. 88(2), pages 302-320, August.
    6. Korobilis, Dimitris, 2018. "Machine Learning Macroeconometrics A Primer," Essex Finance Centre Working Papers 22666, University of Essex, Essex Business School.
    7. Jiacheng Miao & Hanmin Guo & Gefei Song & Zijie Zhao & Lin Hou & Qiongshi Lu, 2023. "Quantifying portable genetic effects and improving cross-ancestry genetic prediction with GWAS summary statistics," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    8. Vincent Fortuin, 2022. "Priors in Bayesian Deep Learning: A Review," International Statistical Review, International Statistical Institute, vol. 90(3), pages 563-591, December.
    9. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon T. Willard, 2021. "The Horseshoe-Like Regularization for Feature Subset Selection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 185-214, May.
    10. Arnab Kumar Maity & Sanjib Basu & Santu Ghosh, 2021. "Bayesian criterion‐based variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 835-857, August.
    11. Costola, Michele & Iacopini, Matteo & Wichers, Casper, 2023. "Bayesian SAR model with stochastic volatility and multiple time-varying weights," SAFE Working Paper Series 407, Leibniz Institute for Financial Research SAFE.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    2. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    3. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    4. Adam N. Smith & Jim E. Griffin, 2023. "Shrinkage priors for high-dimensional demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 21(1), pages 95-146, March.
    5. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Gagnon, Philippe & Wang, Yuxi, 2024. "Robust heavy-tailed versions of generalized linear models with applications in actuarial science," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    7. Matthew F. Dixon & Nicholas G. Polson & Kemen Goicoechea, 2022. "Deep Partial Least Squares for Empirical Asset Pricing," Papers 2206.10014, arXiv.org.
    8. 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.
    9. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    10. Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.
    11. J. A. A. Andrade & Edward Omey, 2017. "Bayesian robustness modelling using the O-regularly varying distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 168-183, August.
    12. J. Andrade & Edward Omey, 2013. "Modelling conflicting information using subexponential distributions and related classes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 491-511, June.
    13. Sylvia Fruhwirth-Schnatter & Peter Knaus, 2022. "Sparse Bayesian State-Space and Time-Varying Parameter Models," Papers 2207.12147, arXiv.org.
    14. Guhaniyogi, Rajarshi, 2017. "Convergence rate of Bayesian supervised tensor modeling with multiway shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 157-168.
    15. Annalisa Cadonna & Sylvia Fruhwirth-Schnatter & Peter Knaus, 2019. "Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models," Papers 1912.03100, arXiv.org.
    16. Mihaela Simionescu, 2021. "Italexit and the Impact of Immigrants from Italy on the Italian Labor Market," JRFM, MDPI, vol. 14(1), pages 1-14, January.
    17. Nicholas G. Polson & James G. Scott, 2016. "Mixtures, envelopes and hierarchical duality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 701-727, September.
    18. Hamura, Yasuyuki & Irie, Kaoru & Sugasawa, Shonosuke, 2022. "Log-regularly varying scale mixture of normals for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:955-969.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.