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Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach

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  • David T. Frazier

Abstract

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately yields inefficient inference; 2) a possible lack of robustness to deviations from the underlying model structure. Motivated by these efficiency and robustness concerns, we construct a new Bayesian method that can deliver efficient estimators when the underlying model is well-specified, and which is simultaneously robust to certain forms of model misspecification. This new approach bypasses the calculation of summaries by considering a norm between empirical and simulated probability measures. For specific choices of the norm, we demonstrate that this approach can deliver point estimators that are as efficient as those obtained using exact Bayesian inference, while also simultaneously displaying robustness to deviations from the underlying model assumptions.

Suggested Citation

  • David T. Frazier, 2020. "Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach," Papers 2006.14126, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14126
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Jeffrey W. Miller & David B. Dunson, 2019. "Robust Bayesian Inference via Coarsening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1113-1125, July.
    3. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    4. Wentao Li & Paul Fearnhead, 2018. "On the asymptotic efficiency of approximate Bayesian computation estimators," Biometrika, Biometrika Trust, vol. 105(2), pages 285-299.
    5. Espen Bernton & Pierre E. Jacob & Mathieu Gerber & Christian P. Robert, 2019. "Approximate Bayesian computation with the Wasserstein distance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 235-269, April.
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    Cited by:

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