  When complex Bayesian models exhibit implausible behaviour, one solution is
to assemble available information into an informative prior. Challenges arise
as prior information is often only available for the observable quantity, or
some model-derived marginal quantity, rather than directly pertaining to the
natural parameters in our model. We propose a method for translating available
prior information, in the form of an elicited distribution for the observable
or model-derived marginal quantity, into an informative joint prior. Our
approach proceeds given a parametric class of prior distributions with as yet
undetermined hyperparameters, and minimises the difference between the supplied
elicited distribution and corresponding prior predictive distribution. We
employ a global, multi-stage Bayesian optimisation procedure to locate optimal
values for the hyperparameters. Three examples illustrate our approach: a
cure-fraction survival model, where censoring implies that the observable
quantity is a priori a mixed discrete/continuous quantity; a setting in which
prior information pertains to $R^{2}$ -- a model-derived quantity; and a
nonlinear regression model.
