IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v187y2023ics0167947323001068.html
   My bibliography  Save this article

The tenets of quantile-based inference in Bayesian models

Author

Listed:
  • Perepolkin, Dmytro
  • Goodrich, Benjamin
  • Sahlin, Ullrika

Abstract

Bayesian inference can be extended to probability distributions defined in terms of their inverse distribution function, i.e. their quantile function. This applies to both prior and likelihood. Quantile-based likelihood is useful in models with sampling distributions which lack an explicit probability density function. Quantile-based prior allows for flexible distributions to express expert knowledge. The principle of quantile-based Bayesian inference is demonstrated in the univariate setting with a Govindarajulu likelihood, as well as in a parametric quantile regression, where the error term is described by a quantile function of a Flattened Skew-Logistic distribution.

Suggested Citation

  • Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:csdana:v:187:y:2023:i:c:s0167947323001068
    DOI: 10.1016/j.csda.2023.107795
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323001068
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107795?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. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Jason C. Reinhardt & Xi Chen & Wenhao Liu & Petar Manchev & M. Elisabeth Paté‐Cornell, 2016. "Asteroid Risk Assessment: A Probabilistic Approach," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 244-261, February.
    3. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    5. Christopher C. Drovandi & Anthony N. Pettitt & Malcolm J. Faddy, 2011. "Approximate Bayesian computation using indirect inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(3), pages 317-337, May.
    6. Warren Gilchrist, 2008. "Regression Revisited," International Statistical Review, International Statistical Institute, vol. 76(3), pages 401-418, December.
    7. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    8. Jonah Gabry & Daniel Simpson & Aki Vehtari & Michael Betancourt & Andrew Gelman, 2019. "Visualization in Bayesian workflow," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 389-402, February.
    9. Espen Bernton & Pierre E. Jacob & Mathieu Gerber & Christian P. Robert, 2019. "Approximate Bayesian computation with the Wasserstein distance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 235-269, April.
    10. Fournier, B. & Rupin, N. & Bigerelle, M. & Najjar, D. & Iost, A. & Wilcox, R., 2007. "Estimating the parameters of a generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2813-2835, March.
    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. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of indirect inference in Bayesian models," OSF Preprints enzgs, Center for Open Science.
    2. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    3. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    4. Muller, Christophe, 2018. "Heterogeneity and nonconstant effect in two-stage quantile regression," Econometrics and Statistics, Elsevier, vol. 8(C), pages 3-12.
    5. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    6. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    7. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    8. Chesher, Andrew, 2017. "Understanding the effect of measurement error on quantile regressions," Journal of Econometrics, Elsevier, vol. 200(2), pages 223-237.
    9. D.T. Frazier & G.M. Martin & C.P. Robert & J. Rousseau, 2016. "Asymptotic Properties of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 18/16, Monash University, Department of Econometrics and Business Statistics.
    10. Kleopatra Nikolaou, 2007. "The behaviour of the real exchange rate: Evidence from regression quantiles," Money Macro and Finance (MMF) Research Group Conference 2006 46, Money Macro and Finance Research Group.
    11. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    12. Jean-Marc Fournier & Isabell Koske, 2012. "The determinants of earnings inequality: evidence from quantile regressions," OECD Journal: Economic Studies, OECD Publishing, vol. 2012(1), pages 7-36.
    13. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    14. Chowdhury, Biplob & Jeyasreedharan, Nagaratnam & Dungey, Mardi, 2018. "Quantile relationships between standard, diffusion and jump betas across Japanese banks," Journal of Asian Economics, Elsevier, vol. 59(C), pages 29-47.
    15. Bouri, Elie & Gupta, Rangan & Tiwari, Aviral Kumar & Roubaud, David, 2017. "Does Bitcoin hedge global uncertainty? Evidence from wavelet-based quantile-in-quantile regressions," Finance Research Letters, Elsevier, vol. 23(C), pages 87-95.
    16. Jamal Bouoiyour & Refk Selmi, 2017. "The Bitcoin price formation: Beyond the fundamental sources," Working Papers hal-01548710, HAL.
    17. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    18. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    19. Wiji Arulampalam & Alison Booth & Mark Bryan, 2010. "Are there asymmetries in the effects of training on the conditional male wage distribution?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 23(1), pages 251-272, January.
    20. Marrocu, Emanuela & Paci, Raffaele & Zara, Andrea, 2015. "Micro-economic determinants of tourist expenditure: A quantile regression approach," Tourism Management, Elsevier, vol. 50(C), pages 13-30.

    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:eee:csdana:v:187:y:2023:i:c:s0167947323001068. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.