IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i9p2541-2556.html
   My bibliography  Save this article

Likelihood-free Bayesian estimation of multivariate quantile distributions

Author

Listed:
  • Drovandi, Christopher C.
  • Pettitt, Anthony N.

Abstract

In this paper, we present new multivariate quantile distributions and utilise likelihood-free Bayesian algorithms for inferring the parameters. In particular, we apply a sequential Monte Carlo (SMC) algorithm that is adaptive in nature and requires very little tuning compared with other approximate Bayesian computation algorithms. Furthermore, we present a framework for the development of multivariate quantile distributions based on a copula. We consider bivariate and time series extensions of the g-and-k distribution under this framework, and develop an efficient component-wise updating scheme free of likelihood functions to be used within the SMC algorithm. In addition, we trial the set of octiles as summary statistics as well as functions of these that form robust measures of location, scale, skewness and kurtosis. We show that these modifications lead to reasonably precise inferences that are more closely comparable to computationally intensive likelihood-based inference. We apply the quantile distributions and algorithms to simulated data and an example involving daily exchange rate returns.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2541-2556
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311001125
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
    2. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    3. Matthias Fischer, 2010. "Generalized Tukey-type distributions with application to financial and teletraffic data," Statistical Papers, Springer, vol. 51(1), pages 41-56, January.
    4. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    5. Knut Heggland & Arnoldo Frigessi, 2004. "Estimating functions in indirect inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 447-462, May.
    6. 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.
    7. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-472, October.
    8. J. Møller & A. N. Pettitt & R. Reeves & K. K. Berthelsen, 2006. "An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants," Biometrika, Biometrika Trust, vol. 93(2), pages 451-458, June.
    9. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    3. 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.
    4. Oh, Man-Suk & Park, Eun Sug & So, Beong-Soo, 2016. "Bayesian variable selection in binary quantile regression," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 177-181.
    5. Marco Bee & Julien Hambuckers & Flavio Santi & Luca Trapin, 2021. "Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach," Computational Statistics, Springer, vol. 36(3), pages 2177-2200, September.
    6. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of indirect inference in Bayesian models," OSF Preprints enzgs, Center for Open Science.
    7. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. 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.
    9. Ajay Jasra, 2015. "Approximate Bayesian Computation for a Class of Time Series Models," International Statistical Review, International Statistical Institute, vol. 83(3), pages 405-435, December.
    10. George Karabatsos, 2023. "Approximate Bayesian computation using asymptotically normal point estimates," Computational Statistics, Springer, vol. 38(2), pages 531-568, June.
    11. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.
    12. 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.
    13. Ong, Victor M.-H. & Nott, David J. & Tran, Minh-Ngoc & Sisson, Scott A. & Drovandi, Christopher C., 2018. "Likelihood-free inference in high dimensions with synthetic likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 271-291.
    14. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    15. 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.

    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. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
    2. Bertl Johanna & Ewing Gregory & Kosiol Carolin & Futschik Andreas, 2017. "Approximate maximum likelihood estimation for population genetic inference," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(5-6), pages 387-405, December.
    3. Henri Pesonen & Umberto Simola & Alvaro Köhn‐Luque & Henri Vuollekoski & Xiaoran Lai & Arnoldo Frigessi & Samuel Kaski & David T. Frazier & Worapree Maneesoonthorn & Gael M. Martin & Jukka Corander, 2023. "ABC of the future," International Statistical Review, International Statistical Institute, vol. 91(2), pages 243-268, August.
    4. Maxime Lenormand & Franck Jabot & Guillaume Deffuant, 2013. "Adaptive approximate Bayesian computation for complex models," Computational Statistics, Springer, vol. 28(6), pages 2777-2796, December.
    5. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    6. repec:dau:papers:123456789/5724 is not listed on IDEAS
    7. Warne, David J. & Baker, Ruth E. & Simpson, Matthew J., 2018. "Multilevel rejection sampling for approximate Bayesian computation," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 71-86.
    8. Drovandi, Christopher C. & McGree, James M. & Pettitt, Anthony N., 2013. "Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 320-335.
    9. Hai‐Dang Dau & Nicolas Chopin, 2022. "Waste‐free sequential Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 114-148, February.
    10. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    11. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.
    12. Filippi Sarah & Barnes Chris P. & Stumpf Michael P.H. & Cornebise Julien, 2013. "On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 87-107, March.
    13. 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.
    14. 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.
    15. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    16. James Martin & Ajay Jasra & Emma McCoy, 2013. "Inference for a class of partially observed point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 413-437, June.
    17. 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.
    18. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    19. Forneron, Jean-Jacques & Ng, Serena, 2018. "The ABC of simulation estimation with auxiliary statistics," Journal of Econometrics, Elsevier, vol. 205(1), pages 112-139.
    20. Edward Herbst & Frank Schorfheide, 2014. "Sequential Monte Carlo Sampling For Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1073-1098, November.
    21. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.

    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:55:y:2011:i:9:p:2541-2556. 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.