IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i2d10.1007_s00180-020-01048-1.html
   My bibliography  Save this article

Bayesian wavelet shrinkage with beta priors

Author

Listed:
  • Alex Rodrigo dos S. Sousa

    (University of São Paulo)

  • Nancy L. Garcia

    (University of Campinas)

  • Brani Vidakovic

    (Texas A&M University)

Abstract

In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this, we present a Bayesian approach for shrinkage of bounded wavelet coefficients in the context of non-parametric regression. We propose the use of a zero-contaminated beta distribution with a support symmetric around zero as the prior distribution for the location parameter in the wavelet domain in models with additive gaussian errors. The hyperparameters of the proposed model are closely related to the shrinkage level, which facilitates their elicitation and interpretation. For signals with a low signal-to-noise ratio, the associated Bayesian shrinkage rules provide significant improvement in performance in simulation studies when compared with standard techniques. Statistical properties such as bias, variance, classical and Bayesian risks of the associated shrinkage rules are presented and their performance is assessed in simulations studies involving standard test functions. Application to real neurological data set on spike sorting is also presented.

Suggested Citation

  • Alex Rodrigo dos S. Sousa & Nancy L. Garcia & Brani Vidakovic, 2021. "Bayesian wavelet shrinkage with beta priors," Computational Statistics, Springer, vol. 36(2), pages 1341-1363, June.
  • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01048-1
    DOI: 10.1007/s00180-020-01048-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-01048-1
    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/s00180-020-01048-1?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. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
    2. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    3. F. Abramovich & T. Sapatinas & B. W. Silverman, 1998. "Wavelet thresholding via a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 725-749.
    Full references (including those not matched with items on IDEAS)

    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. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    2. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
    3. Mahlet G. Tadesse & Joseph G. Ibrahim & Marina Vannucci & Robert Gentleman, 2005. "Wavelet Thresholding with Bayesian False Discovery Rate Control," Biometrics, The International Biometric Society, vol. 61(1), pages 25-35, March.
    4. Stuart Barber & Guy P. Nason, 2004. "Real nonparametric regression using complex wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 927-939, November.
    5. Marco Di Zio & Arnoldo Frigessi, 1999. "Smoothness in Bayesian Non-parametric Regression with Wavelets," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 391-405, December.
    6. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    7. 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.
    8. Martin Guth, 2022. "Predicting Default Probabilities for Stress Tests: A Comparison of Models," Papers 2202.03110, arXiv.org.
    9. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2018. "Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates, 1970-2017," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-14, Economic Statistics Centre of Excellence (ESCoE).
    10. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.
    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. Eric Yanchenko & Howard D. Bondell & Brian J. Reich, 2024. "Spatial regression modeling via the R2D2 framework," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.
    13. 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.
    14. A. Antoniadis, 1997. "Rejoinder," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 143-144, August.
    15. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    16. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    17. 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.
    18. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2020. "Computationally efficient inference in large Bayesian mixed frequency VARs," Economics Letters, Elsevier, vol. 191(C).
    20. Michael Pfarrhofer, 2024. "Forecasts with Bayesian vector autoregressions under real time conditions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(3), pages 771-801, April.

    More about this item

    Statistics

    Access and download 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:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01048-1. 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.