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Multivariate elicitation : association, copulae, and graphical models

Daneshkhah, Alireza and Bedford, Tim (2011) Multivariate elicitation : association, copulae, and graphical models. In: Wiley Encyclopedia of Operations Research and Management Science. John Wiley & Sons Inc.. ISBN 9780470400630

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In practical elicitation problems, we very often wish to elicit from the expert her knowledge about more than one uncertain quantity. When these are considered independent, the uncertainty about them is characterized simply by their marginal distributions; so it is sufficient to elicit the expert's knowledge about the quantities separately. When the independence assumption between the uncertain quantities of interest is not reasonable or has to be explored, the elicitation process becomes more complex. This is where we need to elicit information about the association between the variables in some way. Unfortunately, despite the growing literature about elicitation, this is an area where there is very little guidance to be found. In this article, we present some methods proposed in the literature to specify a multivariate distribution. We focus on the methods that use copulae and vines to construct a joint probability distribution. They enable us to build a multivariate distribution based on the elicited marginal distributions and their dependencies.