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Multilevel rejection sampling for approximate Bayesian computation

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  • Warne, David J.
  • Baker, Ruth E.
  • Simpson, Matthew J.

Abstract

Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate Bayesian computation can be effective techniques for sampling posterior distributions in an approximate Bayesian computation setting. However, without careful consideration of convergence criteria and selection of proposal kernels, such methods can lead to very biased inference or computationally inefficient sampling. In contrast, rejection sampling for approximate Bayesian computation, despite being computationally intensive, results in independent, identically distributed samples from the approximated posterior. An alternative method is proposed for the acceleration of likelihood-free Bayesian inference that applies multilevel Monte Carlo variance reduction techniques directly to rejection sampling. The resulting method retains the accuracy advantages of rejection sampling while significantly improving the computational efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:124:y:2018:i:c:p:71-86
    DOI: 10.1016/j.csda.2018.02.009
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    References listed on IDEAS

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    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. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
    4. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    5. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    6. Beskos, Alexandros & Jasra, Ajay & Law, Kody & Tempone, Raul & Zhou, Yan, 2017. "Multilevel sequential Monte Carlo samplers," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1417-1440.
    7. 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.
    8. repec:dau:papers:123456789/5724 is not listed on IDEAS
    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.
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    Cited by:

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