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Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

Elfadaly, Fadlalla G. and Garthwaite, Paul H. (2017). Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models. Statistics and Computing, 27(2) pp. 449–467.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s11222-016-9632-7
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Abstract

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java.

Item Type: Journal Item
Copyright Holders: 2016 The Authors
ISSN: 0960-3174
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetThe Open University (OU)
Keywords: Dirichlet distribution; Elicitation method; Gaussian copula elicitation; Interactive graphical software; Multinomial model; Prior distribution
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 49480
Depositing User: Fadlalla Elfadaly
Date Deposited: 26 May 2017 08:41
Last Modified: 26 May 2017 08:41
URI: http://oro.open.ac.uk/id/eprint/49480
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