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Eliciting expert judgements about a set of proportions

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  • Rita Esther Zapata-V�zquez
  • Anthony O'Hagan
  • Leonardo Soares Bastos

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.

Suggested Citation

  • Rita Esther Zapata-V�zquez & Anthony O'Hagan & Leonardo Soares Bastos, 2014. "Eliciting expert judgements about a set of proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1919-1933, September.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:9:p:1919-1933
    DOI: 10.1080/02664763.2014.898131
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    Cited by:

    1. Danila Azzolina & Paola Berchialla & Dario Gregori & Ileana Baldi, 2021. "Prior Elicitation for Use in Clinical Trial Design and Analysis: A Literature Review," IJERPH, MDPI, vol. 18(4), pages 1-21, February.
    2. Saurabh Bansal & Genaro J. Gutierrez & Mahesh Nagarajan, 2021. "Theory-Driven Practical Approach to Integrate R&D and Production Planning for Portfolio Management in Agribusiness," Interfaces, INFORMS, vol. 51(5), pages 332-346, September.
    3. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    4. Jiayuan Dong & Jiankan Liao & Xun Huan & Daniel Cooper, 2023. "Expert elicitation and data noise learning for material flow analysis using Bayesian inference," Journal of Industrial Ecology, Yale University, vol. 27(4), pages 1105-1122, August.
    5. Fadlalla G. Elfadaly & Paul H. Garthwaite, 2020. "On quantifying expert opinion about multinomial models that contain covariates," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 959-981, June.

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