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On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction

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  • Matti Vihola
  • Jordan Franks

Abstract

Summary Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure sufficient mixing and post-processing the output, leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators and propose an adaptive approximate Bayesian computation Markov chain Monte Carlo algorithm, which finds a balanced tolerance level automatically based on acceptance rate optimization. Our experiments show that post-processing-based estimators can perform better than direct Markov chain Monte Carlo targeting a fine tolerance, that our confidence intervals are reliable, and that our adaptive algorithm leads to reliable inference with little user specification.

Suggested Citation

  • Matti Vihola & Jordan Franks, 2020. "On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction," Biometrika, Biometrika Trust, vol. 107(2), pages 381-395.
  • Handle: RePEc:oup:biomet:v:107:y:2020:i:2:p:381-395.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz078
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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. George Karabatsos, 2023. "Approximate Bayesian computation using asymptotically normal point estimates," Computational Statistics, Springer, vol. 38(2), pages 531-568, June.
    3. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    4. Duffield, Samuel & Singh, Sumeetpal S., 2022. "Ensemble Kalman inversion for general likelihoods," Statistics & Probability Letters, Elsevier, vol. 187(C).

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