  This article describes an approach to incorporate expert opinion on
observable quantities through the use of a loss function which updates a prior
belief as opposed to specifying parameters on the priors. Eliciting information
on observable quantities allows experts to provide meaningful information on a
quantity familiar to them, in contrast to elicitation on model parameters,
which may be subject to interactions with other parameters or non-linear
transformations before obtaining an observable quantity. The approach to
incorporating expert opinion described in this paper is distinctive in that we
do not specify a prior to match an expert's opinion on observed quantity,
rather we obtain a posterior by updating the model parameters through a loss
function. This loss function contains the observable quantity, expressed a
function of the parameters, and is related to the expert's opinion which is
typically operationalized as a statistical distribution. Parameters which
generate observable quantities which are further from the expert's opinion
incur a higher loss, allowing for the model parameters to be estimated based on
their fidelity to both the data and expert opinion, with the relative strength
determined by the number of observations and precision of the elicited belief.
Including expert opinion in this fashion allows for a flexible specification of
the opinion and in many situations is straightforward to implement with
commonly used probabilistic programming software. We highlight this using three
worked examples of varying model complexity including survival models, a
multivariate normal distribution and a regression problem.
