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Improved approximate Bayesian computation methods via empirical likelihood

Author

Listed:
  • Tatiana Dmitrieva

    (Advocate Aurora Health)

  • Kristin McCullough

    (Grand View University)

  • Nader Ebrahimi

    (Northern Illinois University)

Abstract

Approximate Bayesian Computation (ABC) is a method of statistical inference that is used for complex models where the likelihood function is intractable or computationally difficult, but can be simulated by a computer model. As proposed by Mengersen et al. (Proc Natl Acad Sci 110(4):1321–1326, 2013), when additional information about the parameter of interest is available, empirical likelihood techniques can be used in place of model simulation. In this paper we propose an improvement to Mengersen et al. (2013) ABC via empirical likelihood algorithm through the addition of a testing procedure. We demonstrate the effectiveness of our proposed method through a nanotechnology application where we assess the reliability of nanowires. The efficiency and improved accuracy is shown through simulation analysis.

Suggested Citation

  • Tatiana Dmitrieva & Kristin McCullough & Nader Ebrahimi, 2021. "Improved approximate Bayesian computation methods via empirical likelihood," Computational Statistics, Springer, vol. 36(2), pages 1533-1552, June.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-00985-1
    DOI: 10.1007/s00180-020-00985-1
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    References listed on IDEAS

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    1. Jean-Marie Cornuet & Jean-Michel Marin & Antonietta Mira & Christian P. Robert, 2012. "Adaptive Multiple Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 798-812, December.
    2. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
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    4. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    5. Nader Ebrahimi & Kristin McCullough & Zhili Xiao, 2013. "Reliability of sensors based on nanowire networks," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 215-228.
    6. Maxime Lenormand & Franck Jabot & Guillaume Deffuant, 2013. "Adaptive approximate Bayesian computation for complex models," Computational Statistics, Springer, vol. 28(6), pages 2777-2796, December.
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    8. Blum, Michael G. B., 2010. "Approximate Bayesian Computation: A Nonparametric Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1178-1187.
    Full references (including those not matched with items on IDEAS)

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