IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v82y2020i2d10.1007_s13171-019-00189-w.html
   My bibliography  Save this article

Empirical Priors and Coverage of Posterior Credible Sets in a Sparse Normal Mean Model

Author

Listed:
  • Ryan Martin

    (North Carolina State University)

  • Bo Ning

    (Yale University)

Abstract

Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible sets attain the nominal frequentist coverage probability? This paper investigates the frequentist validity of posterior uncertainty quantification based on a class of empirical priors in the sparse normal mean model. In particular, we show that our marginal posterior credible intervals achieve the nominal frequentist coverage probability under conditions slightly weaker than needed for selection consistency and a Bernstein–von Mises theorem for the full posterior, and numerical investigations suggest that our empirical Bayes method has superior frequentist coverage probability properties compared to other fully Bayes methods.

Suggested Citation

  • Ryan Martin & Bo Ning, 2020. "Empirical Priors and Coverage of Posterior Credible Sets in a Sparse Normal Mean Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 477-498, August.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00189-w
    DOI: 10.1007/s13171-019-00189-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-019-00189-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-019-00189-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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. Nicholas Syring & Ryan Martin, 2019. "Calibrating general posterior credible regions," Biometrika, Biometrika Trust, vol. 106(2), pages 479-486.
    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. Yahia Abdel-Aty & Mohamed Kayid & Ghadah Alomani, 2023. "Generalized Bayes Estimation Based on a Joint Type-II Censored Sample from K-Exponential Populations," Mathematics, MDPI, vol. 11(9), pages 1-11, May.

    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. Onizuka, Takahiro & Iwashige, Fumiya & Hashimoto, Shintaro, 2024. "Bayesian boundary trend filtering," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    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. Martin Feldkircher & Florian Huber & Gary Koop & Michael Pfarrhofer, 2022. "APPROXIMATE BAYESIAN INFERENCE AND FORECASTING IN HUGE‐DIMENSIONAL MULTICOUNTRY VARs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1625-1658, November.
    4. Phella, Anthoulla & Gabriel, Vasco J. & Martins, Luis F., 2024. "Predicting tail risks and the evolution of temperatures," Energy Economics, Elsevier, vol. 131(C).
    5. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    6. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    7. Martin Guth, 2022. "Predicting Default Probabilities for Stress Tests: A Comparison of Models," Papers 2202.03110, arXiv.org.
    8. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    9. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    10. Todd E. Clark & Florian Huber & Gary Koop & Massimiliano Marcellino & Michael Pfarrhofer, 2023. "Tail Forecasting With Multivariate Bayesian Additive Regression Trees," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 979-1022, August.
    11. Chan, Joshua C.C., 2021. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1212-1226.
    12. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    13. Luca Barbaglia & Lorenzo Frattarolo & Niko Hauzenberger & Dominik Hirschbuehl & Florian Huber & Luca Onorante & Michael Pfarrhofer & Luca Tiozzo Pezzoli, 2024. "Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model," Papers 2401.10054, arXiv.org.
    14. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    15. Lukas Berend & Jan Pruser, 2024. "The Transmission of Monetary Policy via Common Cycles in the Euro Area," Papers 2410.05741, arXiv.org, revised Oct 2024.
    16. Anindya Bhadra, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 235-239, June.
    17. Debamita Kundu & Riten Mitra & Jeremy T. Gaskins, 2021. "Bayesian variable selection for multioutcome models through shared shrinkage," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 295-320, March.
    18. Yi Nengjun & Ma Shuangge, 2012. "Hierarchical Shrinkage Priors and Model Fitting for High-dimensional Generalized Linear Models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(6), pages 1-25, November.
    19. You Wu & Jeremy Gaskins & Maiying Kong & Susmita Datta, 2018. "Profiling the effects of short time†course cold ischemia on tumor protein phosphorylation using a Bayesian approach," Biometrics, The International Biometric Society, vol. 74(1), pages 331-341, March.
    20. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.

    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:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00189-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.