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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.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw041
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    References listed on IDEAS

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    1. Nadarajah, Saralees, 2009. "PDFs and Dual PDFs," The American Statistician, American Statistical Association, vol. 63(1), pages 45-48.
    2. 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.
    3. 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.
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    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.

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