Eliciting expert judgements about a set of proportions |
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Authors: | Rita Esther Zapata-Vázquez Anthony O'Hagan Leonardo Soares Bastos |
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Institution: | 1. Probability and Statistics, The University of Sheffield, Western Bank, Sheffield S10 2TN, UK;2. Universidad Autónoma de Yucatán, UIICE, Av. Itzáes 498 x59-A, Mérida, 97000 Mexico;3. IMSS, Ex-Terrenos El Fénix, Mérida, 97150 Mexico;4. Oswaldo Cruz Foundation, Av. Brasil 4365, Manguinhos, Rio de Janeiro, 21040-360 Brazil |
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Abstract: | 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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Keywords: | elicitation Dirichlet distribution SHELF over-fitting multinomial distribution |
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