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Predictive control of posterior robustness for sample size choice in a Bernoulli model

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  • Fulvio De Santis
  • Maria Fasciolo
  • Stefania Gubbiotti

Abstract

In this article we consider the sample size determination problem in the context of robust Bayesian parameter estimation of the Bernoulli model. Following a robust approach, we consider classes of conjugate Beta prior distributions for the unknown parameter. We assume that inference is robust if posterior quantities of interest (such as point estimates and limits of credible intervals) do not change too much as the prior varies in the selected classes of priors. For the sample size problem, we consider criteria based on predictive distributions of lower bound, upper bound and range of the posterior quantity of interest. The sample size is selected so that, before observing the data, one is confident to observe a small value for the posterior range and, depending on design goals, a large (small) value of the lower (upper) bound of the quantity of interest. We also discuss relationships with and comparison to non robust and non informative Bayesian methods. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Fulvio De Santis & Maria Fasciolo & Stefania Gubbiotti, 2013. "Predictive control of posterior robustness for sample size choice in a Bernoulli model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 319-340, August.
    • Handle: RePEc:spr:stmapp:v:22:y:2013:i:3:p:319-340
    DOI: 10.1007/s10260-012-0225-0
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    References listed on IDEAS

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    1. 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.
    2. 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. Ali Karimnezhad & Ahmad Parsian, 2018. "Most stable sample size determination in clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 437-454, August.

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