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On the predictive performance of a non-optimal action in hypothesis testing

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  • Fulvio De Santis

    (Sapienza Università di Roma)

  • Stefania Gubbiotti

    (Sapienza Università di Roma)

Abstract

In Bayesian decision theory, the performance of an action is measured by its posterior expected loss. In some cases it may be convenient/necessary to use a non-optimal decision instead of the optimal one. In these cases it is important to quantify the additional loss we incur and evaluate whether to use the non-optimal decision or not. In this article we study the predictive probability distribution of a relative measure of the additional loss and its use to define sample size determination criteria in a general testing set-up.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:2:d:10.1007_s10260-020-00539-1
    DOI: 10.1007/s10260-020-00539-1
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    References listed on IDEAS

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    1. 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.
    2. M'Lan, Cyr Emile & Joseph, Lawrence & Wolfson, David B., 2006. "Bayesian Sample Size Determination for Case-Control Studies," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 760-772, June.
    3. 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.
    4. 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.
    5. Fulvio De Santis & Stefania Gubbiotti, 2017. "A decision‐theoretic approach to sample size determination under several priors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(3), pages 282-295, May.
    6. 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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