IDEAS home Printed from https://ideas.repec.org/a/spr/jqecon/v20y2022i1d10.1007_s40953-022-00311-0.html
   My bibliography  Save this article

MCMC Convergence for Global-Local Shrinkage Priors

Author

Listed:
  • Kshitij Khare

    (University of Florida)

  • Malay Ghosh

    (University of Florida)

Abstract

Global-local continuous shrinkage priors have emerged as effective and computationally scalable tools for Bayesian sparsity-based regularization in modern high-dimensional settings. These priors have been successfully deployed in various scientific fields, including econometrics. Markov chain Monte Carlo (MCMC) methods are critical for exploring the resulting intractable posterior distributions. In this paper we review the convergence analyses of the corresponding Markov chains, as these analyses are crucial to help understand the quality of the MCMC based approximations of desired posterior quantities. In particular, we discuss unique features of some of these priors which translate into unique and novel choices for the respective convergence analyses. We also describe how these specific examples have served as catalysts for the development of new general techniques for Markov chain convergence analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jqecon:v:20:y:2022:i:1:d:10.1007_s40953-022-00311-0
    DOI: 10.1007/s40953-022-00311-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40953-022-00311-0
    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/s40953-022-00311-0?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. Asmussen, Søren & Glynn, Peter W., 2011. "A new proof of convergence of MCMC via the ergodic theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1482-1485, October.
    2. 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.
    3. 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.
    4. Subahdip Pal & Kshitij Khare & James P. Hobert, 2017. "Trace Class Markov Chains for Bayesian Inference with Generalized Double Pareto Shrinkage Priors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 307-323, June.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    7. 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.
    8. Veronika Ročková & Edward I. George, 2018. "The Spike-and-Slab LASSO," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 431-444, January.
    9. 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.
    10. Gareth O. Roberts & Jeffrey S. Rosenthal, 2001. "Markov Chains and De‐initializing Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 489-504, September.
    11. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    12. Dootika Vats & James M Flegal & Galin L Jones, 2019. "Multivariate output analysis for Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 106(2), pages 321-337.
    13. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    14. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    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. 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).
    2. Banerjee, Sayantan, 2022. "Horseshoe shrinkage methods for Bayesian fusion estimation," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    3. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    4. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    5. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    6. Niloy Biswas & Anirban Bhattacharya & Pierre E. Jacob & James E. Johndrow, 2022. "Coupling‐based convergence assessment of some Gibbs samplers for high‐dimensional Bayesian regression with shrinkage priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 973-996, July.
    7. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    8. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    9. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    10. Minerva Mukhopadhyay & David B. Dunson, 2020. "Targeted Random Projection for Prediction From High-Dimensional Features," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1998-2010, December.
    11. Young Joo Yoon & Cheolwoo Park & Erik Hofmeister & Sangwook Kang, 2012. "Group variable selection in cardiopulmonary cerebral resuscitation data for veterinary patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1605-1621, January.
    12. Shi, Guiling & Lim, Chae Young & Maiti, Tapabrata, 2019. "Model selection using mass-nonlocal prior," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 36-44.
    13. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    14. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    15. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    16. Mike K. P. So & Wing Ki Liu & Amanda M. Y. Chu, 2018. "Bayesian Shrinkage Estimation Of Time-Varying Covariance Matrices In Financial Time Series," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 369-404, December.
    17. Matthew Gentzkow & Bryan T. Kelly & Matt Taddy, 2017. "Text as Data," NBER Working Papers 23276, National Bureau of Economic Research, Inc.
    18. Faisal Maqbool Zahid & Shahla Faisal & Christian Heumann, 2020. "Variable selection techniques after multiple imputation in high-dimensional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 553-580, September.
    19. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    20. 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.

    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:jqecon:v:20:y:2022:i:1:d:10.1007_s40953-022-00311-0. 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.