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Convergence of regression-adjusted approximate Bayesian computation

Author

Listed:
  • Wentao Li
  • Paul Fearnhead

Abstract

SUMMARYWe present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth, one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.

Suggested Citation

  • Wentao Li & Paul Fearnhead, 2018. "Convergence of regression-adjusted approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 105(2), pages 301-318.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:2:p:301-318.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx081
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    Citations

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    Cited by:

    1. Henri Pesonen & Umberto Simola & Alvaro Köhn‐Luque & Henri Vuollekoski & Xiaoran Lai & Arnoldo Frigessi & Samuel Kaski & David T. Frazier & Worapree Maneesoonthorn & Gael M. Martin & Jukka Corander, 2023. "ABC of the future," International Statistical Review, International Statistical Institute, vol. 91(2), pages 243-268, August.
    2. D T Frazier & G M Martin & C P Robert & J Rousseau, 2018. "Asymptotic properties of approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 105(3), pages 593-607.
    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    4. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    5. Yi Liu & Veronika Ročková & Yuexi Wang, 2021. "Variable selection with ABC Bayesian forests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 453-481, July.
    6. 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.

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