Tony O'Hagan - Academic pages - Abstracts

## Nonparametric elicitation for heavy-tailed prior distributions

J.P. Gosling, J.E. Oakley and A. O'Hagan

*University of Sheffield*

**Publication details: **
Submitted to *Bayesian Analysis*.

### Abstract

In the context of statistical analysis, elicitation is the process of
translating someone’s beliefs about some uncertain quantities into a probability
distribution. The person’s judgements about the quantities are usually
fitted to some member of a convenient parametric family. This approach
does not allow for the possibility that any number of distributions could
fit the same judgements.

In this paper, elicitation of an expert’s beliefs is treated as any other
inference problem: the facilitator of the elicitation exercise has prior
beliefs about the form of the expert’s density function, the facilitator elicits
judgements about the density function, and the facilitator’s beliefs about
the expert’s density function are updated in the light of these judgements.
This paper investigates prior beliefs about an expert’s density function
and shows how many different types of judgement can be handled by this
method.

This elicitation method begins with the belief that the expert’s density
will roughly have the shape of a t density. This belief is then updated
through a Gaussian process model using judgements from the expert.
The method gives a framework for quantifying the facilitator’s uncertainty
about a density given judgements about the mean and percentiles of the
expert’s distribution. A property of Gaussian processes can be manipulated
to include judgements about the derivatives of the density, which
allows the facilitator to incorporate mode judgements and judgements on
the sign of the density at any given point. The benefit of including the
second type of judgement is that substantial computational time can be
saved.

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Updated: 16 December 2006
Maintained by: Tony O'Hagan