Test DOI 10.1007/s11749-013-0336-4 ORIGINAL PAPER Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models Fadlalla G. Elfadaly · Paul H. Garthwaite Received: 14 December 2012 / Accepted: 19 June 2013 © Sociedad de Estadística e Investigación Operativa 2013 Abstract This paper addresses the task of eliciting an informative prior distribution for multinomial models. We first introduce a method of eliciting univariate beta distri- butions 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 distribu- tions. 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 pa- rameters 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 F.G. Elfadaly (B ) · P.H. Garthwaite Department of Mathematics and Statistics, The Open University, Milton Keynes, UK e-mail: f.elfadaly@open.ac.uk F.G. Elfadaly Department of Statistics, Cairo University, Cairo, Egypt