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Improving approximate Bayesian computation via quasi Monte Carlo

Author

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  • Alexander Buchholz

    (CREST-ENSAE)

  • Nicolas CHOPIN

    (CREST-ENSAE)

Abstract

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi-Monte Carlo) sequences. We show that the resulting ABC estimates have a lower variance than their Monte Carlo counter-parts. We also develop QMC variants of sequential ABC algorithms, which progressively adapt the proposal distribution and the acceptance threshold. We illustrate our QMC approach through several examples taken from the ABC literature.

Suggested Citation

  • Alexander Buchholz & Nicolas CHOPIN, 2017. "Improving approximate Bayesian computation via quasi Monte Carlo," Working Papers 2017-37, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-37
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    References listed on IDEAS

    as
    1. Simon Barthelmé & Nicolas Chopin, 2014. "Expectation Propagation for Likelihood-Free Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 315-333, March.
    2. 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.
    3. Anthony Lee & Krzysztof Łatuszyński, 2014. "Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 101(3), pages 655-671.
    4. repec:dau:papers:123456789/5724 is not listed on IDEAS
    5. 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.
    6. 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)

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    Cited by:

    1. Jean-Jacques Forneron, 2019. "A Scrambled Method of Moments," Papers 1911.09128, arXiv.org.

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