IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v72y2014i2p153-167.html
   My bibliography  Save this article

A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models

Author

Listed:
  • Stefano Cabras
  • María Castellanos
  • Erlis Ruli

Abstract

Complex models typically involve intractable likelihood functions which, from a Bayesian perspective, lead to intractable posterior distributions. In this context, Approximate Bayesian computation (ABC) methods can be used in order to obtain a valid posterior approximation. However, when simulation from the model is computationally demanding, then the ABC approach may be cumbersome. We discuss an alternative method, where the intractable likelihood is approximated by a quasi-likelihood calculated through an algorithm that is reminiscent of the ABC. The proposed approximation method requires less computational effort than ABC. An extension to multiparameter models is also considered and the method is illustrated by several examples. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Stefano Cabras & María Castellanos & Erlis Ruli, 2014. "A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 153-167, August.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:2:p:153-167
    DOI: 10.1007/s40300-014-0040-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-014-0040-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s40300-014-0040-5?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. Siegmund Kimberly D. & Marjoram Paul & Shibata Darryl, 2008. "Modeling DNA Methylation in a Population of Cancer Cells," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-23, June.
    2. 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.
    3. O. Barndorff-Nielsen, 1995. "Quasi profile and directed likelihoods from estimating functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 461-464, September.
    4. G. Adimari & L. Ventura, 2002. "Quasi-Profile Log Likelihoods for Unbiased Estimating Functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 235-244, June.
    5. Bent Jørgensen & Sven Jesper Knudsen, 2004. "Parameter Orthogonality and Bias Adjustment for Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114, March.
    6. Muhammad Faisal & Andreas Futschik & Ijaz Hussain, 2013. "A new approach to choose acceptance cutoff for approximate Bayesian computation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(4), pages 862-869.
    7. Thomas A. Severini, 2002. "Modified estimating functions," Biometrika, Biometrika Trust, vol. 89(2), pages 333-343, June.
    8. Bortot, P. & Coles, S.G. & Sisson, S.A., 2007. "Inference for Stereological Extremes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 84-92, March.
    9. 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.
    10. Molin Wang, 2003. "Adjusted profile estimating function," Biometrika, Biometrika Trust, vol. 90(4), pages 845-858, December.
    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. 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.
    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 291-312, December.
    3. Gael M. Martin & Brendan P.M. McCabe & David T. Frazier & Worapree Maneesoonthorn & Christian P. Robert, 2016. "Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 09/16, Monash University, Department of Econometrics and Business Statistics.
    4. Buzbas, Erkan O. & Rosenberg, Noah A., 2015. "AABC: Approximate approximate Bayesian computation for inference in population-genetic models," Theoretical Population Biology, Elsevier, vol. 99(C), pages 31-42.
    5. Wilkinson Richard David, 2013. "Approximate Bayesian computation (ABC) gives exact results under the assumption of model error," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(2), pages 129-141, May.
    6. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    7. Thomas A. Dean & Sumeetpal S. Singh & Ajay Jasra & Gareth W. Peters, 2014. "Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 970-987, December.
    8. David T. Frazier & Gael M. Martin & Christian P. Robert, 2015. "On Consistency of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 19/15, Monash University, Department of Econometrics and Business Statistics.
    9. Hanfelt, John J. & Li, Ruosha & Pan, Yi & Payment, Pierre, 2011. "Robust inference for sparse cluster-correlated count data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 182-192, January.
    10. 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.
    11. 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.
    12. 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.
    13. Brenda N Vo & Christopher C Drovandi & Anthony N Pettitt & Graeme J Pettet, 2015. "Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 11(12), pages 1-22, December.
    14. Gael M. Martin & Brendan P.M. McCabe & Worapree Maneesoonthorn & Christian P. Robert, 2014. "Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 20/14, Monash University, Department of Econometrics and Business Statistics.
    15. Muhammad Faisal & Andreas Futschik & Ijaz Hussain & Mitwali Abd-el.Moemen, 2016. "Choosing summary statistics by least angle regression for approximate Bayesian computation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2191-2202, September.
    16. Rodrigues, G.S. & Prangle, D. & Sisson, S.A., 2018. "Recalibration: A post-processing method for approximate Bayesian computation," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 53-66.
    17. Su, Yuandong & Lu, Xinjie & Zeng, Qing & Huang, Dengshi, 2022. "Good air quality and stock market returns," Research in International Business and Finance, Elsevier, vol. 62(C).
    18. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    19. 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.
    20. Lu Wang & Feng Ma & Guoshan Liu, 2020. "Forecasting stock volatility in the presence of extreme shocks: Short‐term and long‐term effects," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(5), pages 797-810, August.

    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:metron:v:72:y:2014:i:2:p:153-167. 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.