On Eliciting Some Prior Distributions for Multinomial Models

On Eliciting Some Prior Distributions for Multinomial Models. Elfadaly, F. G & Garthwaite, P. H
abstract bibtex

In Bayesian analysis of multinomial models, an important assessment task is to elicit an informative joint prior distribution for multinomial probabilities. We start by introducing a method to elicit a univariate beta distribution for the probability of each category using probability quartiles. Three diﬀerent multivariate priors are introduced using the elicited betas. As a tractable conjugate prior, we elicit the hyperparameters of the Dirichlet distribution from those of the univariate betas through some forms of reconciliation using least-squares techniques. However, the Dirichlet distribution is not ﬂexible enough to represent prior information. So, the proposed method is also designed to elicit a generalized Dirichlet distribution, known as Connor-Mosimann distribution, which is also a conjugate prior that has a larger number of parameters and hence a more ﬂexible dependence structure. Moreover, we use the beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals to form their joint multivariate distribution. The proposed method elicits a positive-deﬁnite correlation matrix of this Gaussian copula. All proposed methods are designed to be used with the aid of interactive graphical software written in Java.

@article{elfadaly_eliciting_nodate-1,
	title = {On {Eliciting} {Some} {Prior} {Distributions} for {Multinomial} {Models}},
	abstract = {In Bayesian analysis of multinomial models, an important assessment task is to elicit an informative joint prior distribution for multinomial probabilities. We start by introducing a method to elicit a univariate beta distribution for the probability of each category using probability quartiles. Three diﬀerent multivariate priors are introduced using the elicited betas. As a tractable conjugate prior, we elicit the hyperparameters of the Dirichlet distribution from those of the univariate betas through some forms of reconciliation using least-squares techniques. However, the Dirichlet distribution is not ﬂexible enough to represent prior information. So, the proposed method is also designed to elicit a generalized Dirichlet distribution, known as Connor-Mosimann distribution, which is also a conjugate prior that has a larger number of parameters and hence a more ﬂexible dependence structure. Moreover, we use the beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals to form their joint multivariate distribution. The proposed method elicits a positive-deﬁnite correlation matrix of this Gaussian copula. All proposed methods are designed to be used with the aid of interactive graphical software written in Java.},
	language = {en},
	author = {Elfadaly, Fadlalla G and Garthwaite, Paul H},
	pages = {40},
	file = {Elfadaly and Garthwaite - On Eliciting Some Prior Distributions for Multinom.pdf:/Users/neil.hawkins/Zotero/storage/SYICJ9XR/Elfadaly and Garthwaite - On Eliciting Some Prior Distributions for Multinom.pdf:application/pdf;Elfadaly and Garthwaite - On Eliciting Some Prior Distributions for Multinom.pdf:/Users/neil.hawkins/Zotero/storage/VUBB855W/Elfadaly and Garthwaite - On Eliciting Some Prior Distributions for Multinom.pdf:application/pdf},
}

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