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Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models

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  • Fadlalla Elfadaly
  • Paul Garthwaite

Abstract

This paper addresses the task of eliciting an informative prior distribution for multinomial models. We first introduce a method of eliciting univariate beta distributions for the probability of each category, conditional on the probabilities of other categories. Two different forms of multivariate prior are derived from the elicited beta distributions. First, we determine the hyperparameters of a Dirichlet distribution by reconciling the assessed parameters of the univariate beta conditional distributions. Although the Dirichlet distribution is the standard conjugate prior distribution for multinomial models, it is not flexible enough to represent a broad range of prior information. Second, we use the beta distributions to determine the parameters of a Connor–Mosimann distribution, which is a generalization of a Dirichlet distribution and is also a conjugate prior for multinomial models. It has a larger number of parameters than the standard Dirichlet distribution and hence a more flexible structure. The elicitation methods are designed to be used with the aid of interactive graphical user-friendly software. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Fadlalla Elfadaly & Paul Garthwaite, 2013. "Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 628-646, November.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:4:p:628-646
    DOI: 10.1007/s11749-013-0336-4
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    References listed on IDEAS

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    1. Hankin, Robin K. S., 2010. "A Generalization of the Dirichlet Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i11).
    2. Bunn, Derek W, 1978. "Estimation of a Dirichlet prior distribution," Omega, Elsevier, vol. 6(4), pages 371-373.
    3. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
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    Cited by:

    1. Berthold-Georg Englert & Michael Evans & Gun Ho Jang & Hui Khoon Ng & David Nott & Yi-Lin Seah, 2021. "Checking for model failure and for prior-data conflict with the constrained multinomial model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1141-1168, November.
    2. 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.
    3. 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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