TEST

, Volume 22, Issue 4, pp 628–646 | Cite as

Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models

Original Paper
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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.

Keywords

Elicitation method Prior distribution Dirichlet distribution Connor–Mosimann distribution Multinomial model Interactive graphical software 

Mathematics Subject Classification

62C10 62F15 
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Notes

Acknowledgements

The work reported here was supported by a studentship from the Open University, UK. We are very grateful to Dr. Neville Calleja, Director of Health Information and Research in the Ministry of Health, the Elderly and Community Care, Malta, whose opinion was quantified in the BMI misclassification example.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.Department of StatisticsCairo UniversityCairoEgypt

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