Statistical Methods & Applications

, Volume 22, Issue 3, pp 319–340

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

  • Fulvio De Santis
  • Maria Clara Fasciolo
  • Stefania Gubbiotti
Article

DOI: 10.1007/s10260-012-0225-0

Cite this article as:
De Santis, F., Fasciolo, M.C. & Gubbiotti, S. Stat Methods Appl (2013) 22: 319. doi:10.1007/s10260-012-0225-0
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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.

Keywords

Bayesian robustness Clinical trials Conjugate analysis  Sample size determination 

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fulvio De Santis
    • 1
  • Maria Clara Fasciolo
    • 1
  • Stefania Gubbiotti
    • 1
  1. 1.Dipartimento di Scienze StatisticheSapienza Università di RomaRomaItaly