IDEAS home Printed from https://ideas.repec.org/a/sae/medema/v14y1994i1p46-51.html
   My bibliography  Save this article

Uncertainty in Bayes

Author

Listed:
  • John A. Baron

Abstract

Most standard discussions of Bayes' formula treat sensitivity, specificity, and the prior prob ability as fixed parameters for probability revision, but in fact these usually have associated variability. This in turn generates predictable patterns of uncertainty in the posterior proba bilities. Although these have not been investigated in detail, they have important implications for the interpretation of posterior probabilities and the clinical use of Bayesian probability revision. For a test with a high likelihood ratio for a positive result, the positive predictive value (PPV) is strongly affected by uncertainties in the prior probability when the prior probability is small, but PPV is almost independent of such uncertainties at high values of the prior probability. The PPV is more affected by changes in specificity than by changes in sensitivity, and uncertainty in specificity has its maximal impact on the PPV at low prior probability values. These patterns are most pronounced for tests with high likelihood ratios of positive results. Similar results can be shown for the negative predictive value. These results imply that for suitability good tests, probability revision in certain definable ranges of prior probability may be so strongly affected by errors in the estimations of both the prior probability and the operating characteristics that the posterior probabilities may be unstable in practice. On the other hand, at other values of the prior probability, the posterior probabilities are almost constant, and formal probability revision will not have much impact. These patterns indicate limitations to the reliability and usefulness of calculated posterior probabilities, and have important implications for the clinical use of Bayes' formula. Key words: Bayes' formula; probability revision; posterior probabilities. (Med Decis Making 1994;14:46-51)

Suggested Citation

  • John A. Baron, 1994. "Uncertainty in Bayes," Medical Decision Making, , vol. 14(1), pages 46-51, February.
  • Handle: RePEc:sae:medema:v:14:y:1994:i:1:p:46-51
    DOI: 10.1177/0272989X9401400106
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0272989X9401400106
    Download Restriction: no

    File URL: https://libkey.io/10.1177/0272989X9401400106?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jay J. J. Christensen-Szalanski & Paula H. Diehr & James B. Bushyhead & Robert W. Wood, 1982. "Two Studies of Good Clinical Judgment," Medical Decision Making, , vol. 2(3), pages 275-283, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matt T. Bianchi & Brian M. Alexander & Sydney S. Cash, 2009. "Incorporating Uncertainty Into Medical Decision Making: An Approach to Unexpected Test Results," Medical Decision Making, , vol. 29(1), pages 116-124, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. George R. Bergus & Gretchen B. Chapman & Barcey T. Levy & John W. Ely & Robert A. Oppliger, 1998. "Clinical Diagnosis and the Order of Information," Medical Decision Making, , vol. 18(4), pages 412-417, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:medema:v:14:y:1994:i:1:p:46-51. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.