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The variation of the posterior variance and Bayesian sample size determination

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  • Jörg Martin

    (Physikalisch-Technische Bundesanstalt)

  • Clemens Elster

    (Physikalisch-Technische Bundesanstalt)

Abstract

We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for bounding the posterior variance below a prescribed limit under the true sampling distribution. Compared with sample size determination based on the average of the posterior variance the proposed criterion leads to an increase in sample size and significantly improved success rates. Generic asymptotic properties are proven, such as an asymptotic expression for the sample size and a sort of phase transition. Our study is illustrated using two real world datasets with Poisson and normally distributed data. Based on our results some recommendations are given.

Suggested Citation

  • Jörg Martin & Clemens Elster, 2021. "The variation of the posterior variance and Bayesian sample size determination," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1135-1155, October.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-020-00545-3
    DOI: 10.1007/s10260-020-00545-3
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    References listed on IDEAS

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    1. Ming-Hui Chen & Joseph G. Ibrahim & Peter Lam & Alan Yu & Yuanye Zhang, 2011. "Bayesian Design of Noninferiority Trials for Medical Devices Using Historical Data," Biometrics, The International Biometric Society, vol. 67(3), pages 1163-1170, September.
    2. De Santis, Fulvio, 2006. "Sample Size Determination for Robust Bayesian Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 278-291, March.
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    4. Fulvio De Santis & Marco Perone Pacifico & Valeria Sambucini, 2004. "Optimal predictive sample size for case–control studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 427-441, August.
    5. Fulvio De Santis, 2007. "Using historical data for Bayesian sample size determination," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 95-113, January.
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