Journal
STATISTICS AND COMPUTING
Volume 27, Issue 2, Pages 449-467Publisher
SPRINGER
DOI: 10.1007/s11222-016-9632-7
Keywords
Dirichlet distribution; Elicitation method; Gaussian copula elicitation; Interactive graphical software; Multinomial model; Prior distribution
Funding
- The Open University
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In this paper, we propose novel methods of quantifying expert opinion about prior distributions formultinomial 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.
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