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Bayesian-frequentist sample size determination: a game of two priors

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  • Pierpaolo Brutti
  • Fulvio Santis
  • Stefania Gubbiotti

Abstract

Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter. We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Pierpaolo Brutti & Fulvio Santis & Stefania Gubbiotti, 2014. "Bayesian-frequentist sample size determination: a game of two priors," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 133-151, August.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:2:p:133-151
    DOI: 10.1007/s40300-014-0043-2
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    References listed on IDEAS

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    1. S. K. Sahu & T. M. F. Smith, 2006. "A Bayesian method of sample size determination with practical applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 235-253, March.
    2. Anthony O’Hagan & John W. Stevens, 2001. "Bayesian Assessment of Sample Size for Clinical Trials of Cost-Effectiveness," Medical Decision Making, , vol. 21(3), pages 219-230, May.
    3. 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.
    4. 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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    1. Fulvio De Santis & Stefania Gubbiotti, 2021. "Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials," IJERPH, MDPI, vol. 18(2), pages 1-11, January.
    2. Armando Turchetta & Erica E. M. Moodie & David A. Stephens & Sylvie D. Lambert, 2023. "Bayesian sample size calculations for comparing two strategies in SMART studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2489-2502, September.
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    4. Filip Melinscak & Dominik R Bach, 2020. "Computational optimization of associative learning experiments," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-23, January.
    5. Fulvio De Santis & Stefania Gubbiotti, 2021. "On the predictive performance of a non-optimal action in hypothesis testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 689-709, June.

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