Journal
JOURNAL OF APPLIED STATISTICS
Volume 41, Issue 9, Pages 1919-1933Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02664763.2014.898131
Keywords
elicitation; Dirichlet distribution; SHELF; over-fitting; multinomial distribution
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Funding
- Programa de Mejoramiento del Profesorado (PROMEP)
- Instituto Mexicano del Seguro social (IMSS)
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Eliciting expert knowledge about several uncertain quantities is a complex task when those quantities exhibit associations. A well-known example of such a problem is eliciting knowledge about a set of uncertain proportions which must sum to 1. The usual approach is to assume that the expert's knowledge can be adequately represented by a Dirichlet distribution, since this is by far the simplest multivariate distribution that is appropriate for such a set of proportions. It is also the most convenient, particularly when the expert's prior knowledge is to be combined with a multinomial sample since then the Dirichlet is the conjugate prior family. Several methods have been described in the literature for eliciting beliefs in the form of a Dirichlet distribution, which typically involve eliciting from the expert enough judgements to identify uniquely the Dirichlet hyperparameters. We describe here a new method which employs the device of over-fitting, i.e. eliciting more than the minimal number of judgements, in order to (a) produce a more carefully considered Dirichlet distribution and (b) ensure that the Dirichlet distribution is indeed a reasonable fit to the expert's knowledge. The method has been implemented in a software extension of the Sheffield elicitation framework (SHELF) to facilitate the multivariate elicitation process.
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