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Robust Bayesian Inference via Coarsening

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  • Jeffrey W. Miller
  • David B. Dunson

Abstract

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure. We introduce a novel approach to Bayesian inference that improves robustness to small departures from the model: rather than conditioning on the event that the observed data are generated by the model, one conditions on the event that the model generates data close to the observed data, in a distributional sense. When closeness is defined in terms of relative entropy, the resulting “coarsened” posterior can be approximated by simply tempering the likelihood—that is, by raising the likelihood to a fractional power—thus, inference can usually be implemented via standard algorithms, and one can even obtain analytical solutions when using conjugate priors. Some theoretical properties are derived, and we illustrate the approach with real and simulated data using mixture models and autoregressive models of unknown order. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:527:p:1113-1125
    DOI: 10.1080/01621459.2018.1469995
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    Citations

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    Cited by:

    1. Ruben Loaiza‐Maya & Gael M. Martin & David T. Frazier, 2021. "Focused Bayesian prediction," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 517-543, August.
    2. Takuo Matsubara & Jeremias Knoblauch & François‐Xavier Briol & Chris J. Oates, 2022. "Robust generalised Bayesian inference for intractable likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 997-1022, July.
    3. Mike G. Tsionas, 2019. "Robust Bayesian Inference in Stochastic Frontier Models," JRFM, MDPI, vol. 12(4), pages 1-9, December.
    4. Tsionas, Mike G., 2023. "Joint production in stochastic non-parametric envelopment of data with firm-specific directions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1336-1347.
    5. Minerva Mukhopadhyay & Didong Li & David B. Dunson, 2020. "Estimating densities with non‐linear support by using Fisher–Gaussian kernels," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1249-1271, December.
    6. Mingyung Kim & Eric T. Bradlow & Raghuram Iyengar, 2022. "Selecting Data Granularity and Model Specification Using the Scaled Power Likelihood with Multiple Weights," Marketing Science, INFORMS, vol. 41(4), pages 848-866, July.
    7. David T. Frazier & Ruben Loaiza-Maya & Gael M. Martin & Bonsoo Koo, 2021. "Loss-Based Variational Bayes Prediction," Monash Econometrics and Business Statistics Working Papers 8/21, Monash University, Department of Econometrics and Business Statistics.
    8. 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.
    9. 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.
    10. David T. Frazier, 2020. "Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach," Papers 2006.14126, arXiv.org.
    11. Yahia Abdel-Aty & Mohamed Kayid & Ghadah Alomani, 2023. "Generalized Bayes Estimation Based on a Joint Type-II Censored Sample from K-Exponential Populations," Mathematics, MDPI, vol. 11(9), pages 1-11, May.

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