IDEAS home Printed from https://ideas.repec.org/p/osf/osfxxx/enzgs.html
   My bibliography  Save this paper

The tenets of indirect inference in Bayesian models

Author

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

Abstract

This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful

Suggested Citation

  • Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of indirect inference in Bayesian models," OSF Preprints enzgs, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:enzgs
    DOI: 10.31219/osf.io/enzgs
    as

    Download full text from publisher

    File URL: https://osf.io/download/613b44893d2d6a01e89fd92b/
    Download Restriction: no
    File URL: https://libkey.io/10.31219/osf.io/enzgs?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
    ---><---

    References listed on IDEAS

    as
    1. Thomas W. Keelin, 2016. "The Metalog Distributions," Decision Analysis, INFORMS, vol. 13(4), pages 243-277, December.
    2. Christopher C. Hadlock & J. Eric Bickel, 2017. "Johnson Quantile-Parameterized Distributions," Decision Analysis, INFORMS, vol. 14(1), pages 35-64, March.
    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. Saralees Nadarajah, 2009. "Bathtub-shaped failure rate functions," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 855-863, September.
    5. 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.
    6. N.N. Midhu & P.G. Sankaran & N. Unnikrishnan Nair, 2014. "A Class of Distributions with Linear Hazard Quantile Function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(17), pages 3674-3689, September.
    7. Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    8. Mahmoud Aldeni & Carl Lee & Felix Famoye, 2017. "Families of distributions arising from the quantile of generalized lambda distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-18, December.
    9. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    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 & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.
    2. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    3. 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.
    4. Kobayashi, Genya, 2014. "A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 167-183.
    5. Lorenzo Pacchiardi & Pierre Künzli & Marcel Schöngens & Bastien Chopard & Ritabrata Dutta, 2021. "Distance-learning For Approximate Bayesian Computation To Model a Volcanic Eruption," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 288-317, May.
    6. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
    7. Anthony Ebert & Ritabrata Dutta & Kerrie Mengersen & Antonietta Mira & Fabrizio Ruggeri & Paul Wu, 2021. "Likelihood‐free parameter estimation for dynamic queueing networks: Case study of passenger flow in an international airport terminal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 770-792, June.
    8. 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.
    9. Menéndez, P. & Fan, Y. & Garthwaite, P.H. & Sisson, S.A., 2014. "Simultaneous adjustment of bias and coverage probabilities for confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 35-44.
    10. Jonathan U Harrison & Ruth E Baker, 2020. "An automatic adaptive method to combine summary statistics in approximate Bayesian computation," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-21, August.
    11. Dyer, Joel & Cannon, Patrick & Farmer, J. Doyne & Schmon, Sebastian M., 2024. "Black-box Bayesian inference for agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 161(C).
    12. repec:bla:istatr:v:83:y:2015:i:3:p:405-435 is not listed on IDEAS
    13. Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    14. Ninna Vihrs & Jesper Møller & Alan E. Gelfand, 2022. "Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 185-210, March.
    15. Grazzini, Jakob & Richiardi, Matteo G. & Tsionas, Mike, 2017. "Bayesian estimation of agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 26-47.
    16. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    17. 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.
    18. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.
    19. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.
    20. P.G. Sankaran & N.N. Midhu, 2017. "Nonparametric estimation of mean residual quantile function under right censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(10), pages 1856-1874, July.
    21. Mathias Silva, 2023. "Parametric models of income distributions integrating misreporting and non-response mechanisms," AMSE Working Papers 2311, Aix-Marseille School of Economics, France.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:osf:osfxxx:enzgs. 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: OSF (email available below). General contact details of provider: https://osf.io/preprints/ .

    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.