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Multi-pass Bayesian estimation: a robust Bayesian method

Author

Listed:
  • Yeming Lei

    (The University of Queensland
    CSIRO)

  • Shijie Zhou

    (CSIRO)

  • Jerzy Filar

    (The University of Queensland)

  • Nan Ye

    (The University of Queensland)

Abstract

The prior plays a central role in Bayesian inference but specifying a prior is often difficult and a prior considered appropriate by a modeler may be significantly biased. We propose multi-pass Bayesian estimation (MBE), a robust Bayesian method capable of adjusting the prior’s influence on the inference result based on the prior’s quality. MBE adjusts the relative importance of the prior and the data by iteratively performing approximate Bayesian updates on the given data, with the number of updates determined using a cross-validation method. The repeated use of the data resembles the data cloning method, but data cloning performs maximum likelihood estimation (MLE), while MBE interpolates between standard Bayesian inference and MLE; there are also algorithmic differences in how MBE and data cloning make repeated use of the data. Alternatively, MBE can be considered a method for constructing a new prior from the given initial prior and the data. We additionally provide a new non-asymptotic bound on the convergence of data cloning, and provide an MBE-like iterative heuristic approach which achieves faster convergence speed by boosting posterior variance. In numerical simulations on several simulated and real-world datasets, MBE provides robust inference results as compared to standard Bayesian inference and MLE.

Suggested Citation

  • Yeming Lei & Shijie Zhou & Jerzy Filar & Nan Ye, 2024. "Multi-pass Bayesian estimation: a robust Bayesian method," Computational Statistics, Springer, vol. 39(4), pages 2183-2216, June.
  • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01390-0
    DOI: 10.1007/s00180-023-01390-0
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    References listed on IDEAS

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    1. Jukka Corander & Jukka Sirén & Elja Arjas, 2008. "Bayesian spatial modeling of genetic population structure," Computational Statistics, Springer, vol. 23(1), pages 111-129, January.
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    3. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
    4. J. L. Brown & L. B. Hund, 2018. "Estimating material properties under extreme conditions by using Bayesian model calibration with functional outputs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 1023-1045, August.
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