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Sequential Monte Carlo for cut-Bayesian posterior computation

Author

Listed:
  • Joseph Mathews

    (Duke University
    Los Alamos National Laboratory)

  • Giri Gopalan

    (Los Alamos National Laboratory)

  • James Gattiker

    (Los Alamos National Laboratory)

  • Sean Smith

    (Los Alamos National Laboratory)

  • Devin Francom

    (Los Alamos National Laboratory)

Abstract

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method and apply these results to a realistic setting where a computer model is misspecified. Two theoretically justified variations are presented for making the sequential Monte Carlo estimator more computationally efficient, based on linear tempering and finding suitable permutations of initial parameter draws. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

Suggested Citation

  • Joseph Mathews & Giri Gopalan & James Gattiker & Sean Smith & Devin Francom, 2025. "Sequential Monte Carlo for cut-Bayesian posterior computation," Computational Statistics, Springer, vol. 40(5), pages 2749-2779, June.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:5:d:10.1007_s00180-024-01576-0
    DOI: 10.1007/s00180-024-01576-0
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    References listed on IDEAS

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    1. Liang, Faming & Liu, Chuanhai & Carroll, Raymond J., 2007. "Stochastic Approximation in Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 305-320, March.
    2. Garland Durham & John Geweke, 2014. "Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments," Advances in Econometrics, in: Bayesian Model Comparison, volume 34, pages 1-44, Emerald Group Publishing Limited.
    3. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    4. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    5. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.
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