Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

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• 作者：Fadlalla G. Elfadaly ; Paul H. Garthwaite
• 关键词：Dirichlet distribution ; Elicitation method ; Gaussian copula elicitation ; Interactive graphical software ; Multinomial model ; Prior distribution
• 刊名：Statistics and Computing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：27
• 期：2
• 页码：449-467
• 全文大小：1464KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science;
• 出版者：Springer US
• ISSN：1573-1375
• 卷排序：27

文摘

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.