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Frequentist accuracy of Bayesian estimates

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  • Bradley Efron

Abstract

type="main" xml:id="rssb12080-abs-0001"> In the absence of relevant prior experience, popular Bayesian estimation techniques usually begin with some form of ‘uninformative’ prior distribution intended to have minimal inferential influence. The Bayes rule will still produce nice looking estimates and credible intervals, but these lack the logical force that is attached to experience-based priors and require further justification. The paper concerns the frequentist assessment of Bayes estimates. A simple formula is shown to give the frequentist standard deviation of a Bayesian point estimate. The same simulations as required for the point estimate also produce the standard deviation. Exponential family models make the calculations particularly simple and bring in a connection to the parametric bootstrap.

Suggested Citation

  • Bradley Efron, 2015. "Frequentist accuracy of Bayesian estimates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(3), pages 617-646, June.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:3:p:617-646
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-3
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    Cited by:

    1. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    2. DongHyuk Lee & Raymond J. Carroll & Samiran Sinha, 2017. "Frequentist standard errors of Bayes estimators," Computational Statistics, Springer, vol. 32(3), pages 867-888, September.
    3. Elsa Vazquez & Jeffrey R. Wilson, 2021. "Partitioned method of valid moment marginal model with Bayes interval estimates for correlated binary data with time-dependent covariates," Computational Statistics, Springer, vol. 36(4), pages 2701-2718, December.
    4. Jack P. C. Kleijnen & Wim C. M. van Beers, 2022. "Statistical Tests for Cross-Validation of Kriging Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 607-621, January.
    5. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    6. De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2022. "Sampling properties of the Bayesian posterior mean with an application to WALS estimation," Journal of Econometrics, Elsevier, vol. 230(2), pages 299-317.
    7. Kleijnen, Jack & van Nieuwenhuyse, I. & van Beers, W.C.M., 2022. "Constrained Optimization in Simulation : Efficient Global Optimization and Karush-Kuhn-Tucker Conditions (revision of 2021-031)," Discussion Paper 2022-015, Tilburg University, Center for Economic Research.
    8. Franks Alexander M. & D’Amour Alexander & Cervone Daniel & Bornn Luke, 2016. "Meta-analytics: tools for understanding the statistical properties of sports metrics," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(4), pages 151-165, December.
    9. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    10. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    11. Matthew Reimherr & Xiao‐Li Meng & Dan L. Nicolae, 2021. "Prior sample size extensions for assessing prior impact and prior‐likelihood discordance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 413-437, July.
    12. Andres Ramirez-Hassan & Manuel Correa-Giraldo, 2018. "Focused econometric estimation for noisy and small datasets: A Bayesian Minimum Expected Loss estimator approach," Papers 1809.06996, arXiv.org.

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