摘要：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 tted to
some member of a convenient parametric family. This approach does not allow for
the possibility that any number of distributions could t 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 up-
dated in the light of these judgements. This paper investigates prior beliefs about
an expert's density function and shows how many di
erent 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 judge-
ments about the mean and percentiles of the expert's distribution. A property of
Gaussian processes can be manipulated to include judgements about the deriva-
tives of the density, which allows the facilitator to incorporate mode judgements
and judgements on the sign of the density at any given point. The bene t of in-
cluding the second type of judgement is that substantial computational time can
be saved.
关键词：Expert elicitation, Gaussian process, heavy-tailed distribution, non-
parametric density estimation.
