Tony O'Hagan - Academic pages - Abstracts

## Eliciting Expert Judgements about a Set of Proportions

Rita Zapata-Vazquez, Anthony O’Hagan and Leo Soares Bastos

*School of Mathematics and Statistics, University of Sheffield, UK*,
*Facultad de Medicina, Universidad Autonoma de Yucatan, Mexico* and
*Scientific Computational Program, Oswaldo Cruz Foundation, Brazil*

**Publication details: **
*Journal of Appplied Statistics* **41**, 1919-1933, 2014.

### Abstract

Eliciting expert knowledge about several uncertain quantities is a complex task when those
quantities exhibit associations. A well-known example of such a problem is eliciting knowledge
about a set of uncertain proportions which must sum to 1. The usual approach is to assume
that the expert's knowledge can be adequately represented by a Dirichlet distribution, since
this is by far the simplest multivariate distribution that is appropriate for such a set of
proportions. It is also the most convenient, particularly when the expert's prior knowledge
is to be combined with a multinomial sample since then the Dirichlet is the conjugate prior
family.

Several methods have been described in the literature for eliciting beliefs in the form of a
Dirichlet distribution, which typically involve eliciting from the expert enough judgements to
identify uniquely the Dirichlet hyperparameters.

We describe here a new method which employs the device of over-fitting, i.e. eliciting more
than the minimal number of judgements, in order to (a) produce a more carefully considered
Dirichlet distribution and (b) ensure that the Dirichlet distribution is indeed a reasonable fit
to the expert's knowledge. The method has been implemented in a software extension of the
Sheffield Elicitation Framework (SHELF) to facilitate the multivariate elicitation process.

**Keywords:** elicitation; Dirichlet distribution; SHELF; over-fitting.

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Updated: 8 July 2014
Maintained by: Tony O'Hagan