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Sensitivity of Bayes Procedures to the Prior Distribution

Author

Listed:
  • Donald A. Pierce

    (Oregon State University, Corvallis, Oregon)

  • J. Leroy Folks

    (Oklahoma State University, Stillwater, Oklahoma)

Abstract

In the statistical decision problem, let p 0 be a given prior probability distribution and d 0 be the Bayes decision function under p 0 . Our basic approach is to find the nearest distribution to p 0 for which the optimal decision function would lead to an expected saving of some fixed amount ϵ over using d 0 . Hence, for any prior distribution nearer to p 0 than this one, do is ϵ-Bayes. This sensitivity analysis is considered from two viewpoints, before and after performing the experiment. These results constitute a modification and extension of some recent results by Fishburn, Murphy, and Isaacs, and we make use of their basic approach and computing algorithm. Our modifications are applicable to their problem as well.

Suggested Citation

  • Donald A. Pierce & J. Leroy Folks, 1969. "Sensitivity of Bayes Procedures to the Prior Distribution," Operations Research, INFORMS, vol. 17(2), pages 344-350, April.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:2:p:344-350
    DOI: 10.1287/opre.17.2.344
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    Cited by:

    1. Stanca, Lorenzo, 2023. "Robust Bayesian choice," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 94-106.
    2. Anderson, Jock R. & Hardaker, J. Brian, 1972. "An Appreciation of Decision Analysis in Management," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(04), pages 1-15, December.
    3. Stanca Lorenzo, 2023. "Robust Bayesian Choice," Working papers 079, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    4. Lorenzo Stanca, 2023. "Robust Bayesian Choice," Carlo Alberto Notebooks 690 JEL Classification: C, Collegio Carlo Alberto.

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