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The role of informative priors in zero-numerator problems: Being conservative versus being candid

Publication ,  Journal Article
Winkler, RL; Smith, JE; Fryback, DG
Published in: American Statistician
January 1, 2002

The "Rule of Three" gives an approximation for an upper 95% confidence bound for a proportion in a zero-numerator problem, which occurs when the observed relative frequency is zero. We compare the results from the Rule of Three with those from a Bayesian approach with noninformative and informative priors. Informative priors are especially valuable in zero-numerator problems because they can represent the available information and because different noninformative priors can give conflicting advice. Moreover, the use of upper 95% bounds and noninformative priors in an effort to be conservative may backfire when the values are used in further predictive or decision-theoretic calculations. It is better to be candid than conservative, using all of the information available in forming the prior and considering the uncertainty represented by the full posterior distribution.

Duke Scholars

Published In

American Statistician

DOI

ISSN

0003-1305

Publication Date

January 1, 2002

Volume

56

Issue

1

Start / End Page

1 / 4

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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ICMJE
MLA
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Winkler, R. L., Smith, J. E., & Fryback, D. G. (2002). The role of informative priors in zero-numerator problems: Being conservative versus being candid. American Statistician, 56(1), 1–4. https://doi.org/10.1198/000313002753631295
Winkler, R. L., J. E. Smith, and D. G. Fryback. “The role of informative priors in zero-numerator problems: Being conservative versus being candid.” American Statistician 56, no. 1 (January 1, 2002): 1–4. https://doi.org/10.1198/000313002753631295.
Winkler RL, Smith JE, Fryback DG. The role of informative priors in zero-numerator problems: Being conservative versus being candid. American Statistician. 2002 Jan 1;56(1):1–4.
Winkler, R. L., et al. “The role of informative priors in zero-numerator problems: Being conservative versus being candid.” American Statistician, vol. 56, no. 1, Jan. 2002, pp. 1–4. Scopus, doi:10.1198/000313002753631295.
Winkler RL, Smith JE, Fryback DG. The role of informative priors in zero-numerator problems: Being conservative versus being candid. American Statistician. 2002 Jan 1;56(1):1–4.
Journal cover image

Published In

American Statistician

DOI

ISSN

0003-1305

Publication Date

January 1, 2002

Volume

56

Issue

1

Start / End Page

1 / 4

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics