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Eliciting density ratio classes

Publication ,  Journal Article
Rinderknecht, SL; Borsuk, ME; Reichert, P
Published in: International Journal of Approximate Reasoning
September 1, 2011

The probability distributions of uncertain quantities needed for predictive modelling and decision support are frequently elicited from subject matter experts. However, experts are often uncertain about quantifying their beliefs using precise probability distributions. Therefore, it seems natural to describe their uncertain beliefs using sets of probability distributions. There are various possible structures, or classes, for defining set membership of continuous random variables. The Density Ratio Class has desirable properties, but there is no established procedure for eliciting this class. Thus, we propose a method for constructing Density Ratio Classes that builds on conventional quantile or probability elicitation, but allows the expert to state intervals for these quantities. Parametric shape functions, ideally also suggested by the expert, are then used to bound the nonparametric set of shapes of densities that belong to the class and are compatible with the stated intervals. This leads to a natural metric for the size of the class based on the ratio of the total areas under upper and lower bounding shape functions. This ratio will be determined by the characteristics of the shape functions, the scatter of the elicited values, and the explicit expert imprecision, as characterized by the width of the stated intervals. We provide some examples, both didactic and real, and conclude with recommendations for the further development and application of the Density Ratio Class. © 2011 Elsevier Inc. All rights reserved.

Duke Scholars

Published In

International Journal of Approximate Reasoning

DOI

ISSN

0888-613X

Publication Date

September 1, 2011

Volume

52

Issue

6

Start / End Page

792 / 804

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4602 Artificial intelligence
  • 0801 Artificial Intelligence and Image Processing
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

Citation

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Rinderknecht, S. L., Borsuk, M. E., & Reichert, P. (2011). Eliciting density ratio classes. International Journal of Approximate Reasoning, 52(6), 792–804. https://doi.org/10.1016/j.ijar.2011.02.002
Rinderknecht, S. L., M. E. Borsuk, and P. Reichert. “Eliciting density ratio classes.” International Journal of Approximate Reasoning 52, no. 6 (September 1, 2011): 792–804. https://doi.org/10.1016/j.ijar.2011.02.002.
Rinderknecht SL, Borsuk ME, Reichert P. Eliciting density ratio classes. International Journal of Approximate Reasoning. 2011 Sep 1;52(6):792–804.
Rinderknecht, S. L., et al. “Eliciting density ratio classes.” International Journal of Approximate Reasoning, vol. 52, no. 6, Sept. 2011, pp. 792–804. Scopus, doi:10.1016/j.ijar.2011.02.002.
Rinderknecht SL, Borsuk ME, Reichert P. Eliciting density ratio classes. International Journal of Approximate Reasoning. 2011 Sep 1;52(6):792–804.
Journal cover image

Published In

International Journal of Approximate Reasoning

DOI

ISSN

0888-613X

Publication Date

September 1, 2011

Volume

52

Issue

6

Start / End Page

792 / 804

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4602 Artificial intelligence
  • 0801 Artificial Intelligence and Image Processing
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics