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Biometrika Advance Access originally published online on May 13, 2007
Biometrika 2007 94(2):427-441; doi:10.1093/biomet/asm031
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Copyright © 2007 Biometrika Trust

Articles

Uncertainty in prior elicitations: a nonparametric approach

Jeremy E. Oakley and Anthony O'Hagan

Department of Probability and Statistics, University of Sheffield, Sheffield, S3 7RH, U.K.

j.oakley{at}sheffield.ac.uk

a.ohagan{at}sheffield.ac.uk

Received for publication 1 July 2005. Revision received 1 October 2006.
  Abstract

A key task in the elicitation of expert knowledge is to construct a distribution from the finite, and usually small, number of statements that have been elicited from the expert. These statements typically specify some quantiles or moments of the distribution. Such statements are not enough to identify the expert's probability distribution uniquely, and the usual approach is to fit some member of a convenient parametric family. There are two clear deficiencies in this solution. First, the expert's beliefs are forced to fit the parametric family. Secondly, no account is then taken of the many other possible distributions that might have fitted the elicited statements equally well. We present a nonparametric approach which tackles both of these deficiencies. We also consider the issue of the imprecision in the elicited probability judgements.

Key Words: Expert elicitation • Gaussian process • Nonparametric density estimation


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