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Improved approximate Bayesian computation methods via empirical likelihood

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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.

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References

  • Beaumont M (2010) Approximate Bayesian computation in evolution and ecology. Annu Rev Ecol Evol Syst 41:379–406

    Article  Google Scholar 

  • Beaumont M, Zhang W, Balding D (2002) Approximate bayesian computation in population genetics. Genetics 162:2025–2035

    Article  Google Scholar 

  • Berkovitz LD (2002) Convexity and optimization in Rn. Wiley, New York

    Book  Google Scholar 

  • Blum M (2010) Approximate bayesian computation: a nonparametric perspective. J Am Stat Assoc 105(491):1178–1187

    Article  MathSciNet  Google Scholar 

  • Cornuet J, Marin J, Mira A, Robert C (2012) Adaptive multiple importance sampling. Scand J Stat 39(4):789–812

    Article  MathSciNet  Google Scholar 

  • Csilléry K, Blum MG, Gaggiotti OE, François O (2010) Approximate bayesian computation (abc) in practice. Trends Ecol Evol 25(7):410–418

    Article  Google Scholar 

  • Drovandi C, Grazian C, Mengersen K, Robert C (2018) Approximating the likelihood in approximate bayesian computation. In: Sisson S, Fan Y, Beaumont M (eds) Handbook of approximate bayesian computation, 1st edn. Chapman and Hall, New York, pp 321–368

    Chapter  Google Scholar 

  • Ebrahimi N, McCullough K (2016) Using approximate bayesian computation to assess the reliability of nanocomponents of a nanosystem. Int J Reliab Q Saf Eng 23:1650009

    Article  Google Scholar 

  • Ebrahimi N, McCullough K, Xiao Z (2013) Reliability of sensors based on nanowire networks. IIE Trans 45(2):215–228

    Article  Google Scholar 

  • Jarvenpaa M, Gutmann M, Vehtari A, P M (2018) Gaussian process modeling in approximate bayesian computation to estimate horizontal gene transfer in bacteria. Ann Appl Stat (to appear)

  • Lazar NA (2003) Bayesian empirical likelihood. Biometrika 90(2):319–326

    Article  MathSciNet  Google Scholar 

  • Lenormand M, Jabot F, Deffuant G (2013) Adaptive approximate bayesian computation for complex models. Comput Stat 28(6):2777–2796

    Article  MathSciNet  Google Scholar 

  • Marin J, Pudlo P, Robert CP, Ryder RJ (2012) Approximate bayesian computational methods. Stat Comput 22(6):1167–1180

    Article  MathSciNet  Google Scholar 

  • Masuda H, Ashoh H, Watanabe M, Nishio K, Nakao M, Tamamura T (2001) Square and triangular nanohole array architectures in anodic alumina. Adv Mater 13(3):189–192

    Article  Google Scholar 

  • Mengersen KL, Pudlo P, Robert CP (2013) Bayesian computation via empirical likelihood. Proc Natl Acad Sci 110(4):1321–1326

    Article  Google Scholar 

  • Moon HR, Schorfheide F (2007) Boosting your instruments: estimation with overidentifying inequality moment conditions. IEPR working paper no. 06.56

  • Owen AB (2001) Empirical likelihood. Chapman and Hall, Boca Raton

    Book  Google Scholar 

  • Roding M, Zagato E, Remaut K, Braeckmans K (2016) Approximate bayesian computation for estimating number concentrations of monodisperse nanoparticles in suspension by optical microscopy. Phys Rev E 93(6):063311

    Article  Google Scholar 

  • Schennach SM (2005) Bayesian exponentially tilted empirical likelihood. Biometrika 92(1):31–46

    Article  MathSciNet  Google Scholar 

  • Zeng X, Latimer M, Xiao Z, Panuganti S, Welp U, Kwok W, Xu T (2011a) Hydrogen gas sensing with networks of ultrasmall palladium nanowires formed on filtration membranes. Nano Lett 11(1):262–268

    Article  Google Scholar 

  • Zeng X, Latimer M, Xiao Z, Panuganti S, Welp U, Kwok W, Xu T (2011b) Hydrogen gas sensing with networks of ultrasmall palladium nanowires formed on filtration membranes. Nano Lett 11(1):262–268

    Article  Google Scholar 

  • Zhou M (2016) emplik: Empirical likelihood ratio for censored/truncated data. R package version 1.0-3

Download references

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Authors and Affiliations

  1. Advocate Aurora Health, 3075 Highland Parkway, Suite 600, Downers Grove, IL, 60515, USA

    Tatiana Dmitrieva

  2. Grand View University, 1200 Grandview Ave, Des Moines, IA, 50316, USA

    Kristin McCullough

  3. Northern Illinois University, 1425 Lincoln Hwy, DeKalb, IL, 60115, USA

    Nader Ebrahimi

Authors
  1. Tatiana Dmitrieva
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  2. Kristin McCullough
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  3. Nader Ebrahimi
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Correspondence to Nader Ebrahimi.

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Dmitrieva, T., McCullough, K. & Ebrahimi, N. Improved approximate Bayesian computation methods via empirical likelihood. Comput Stat 36, 1533–1552 (2021). https://doi.org/10.1007/s00180-020-00985-1

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  • DOI: https://doi.org/10.1007/s00180-020-00985-1

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