  It can be important in Bayesian analyses of complex models to construct
informative prior distributions which reflect knowledge external to the data at
hand. Nevertheless, how much prior information an analyst can elicit from an
expert will be limited due to constraints of time, cost and other factors. This
paper develops effective numerical methods for exploring reasonable choices of
a prior distribution from a parametric class, when prior information is
specified in the form of some limited constraints on prior predictive
distributions, and where these prior predictive distributions are analytically
intractable. The methods developed may be thought of as a novel application of
the ideas of history matching, a technique developed in the literature on
assessment of computer models. We illustrate the approach in the context of
logistic regression and sparse signal shrinkage prior distributions for
high-dimensional linear models.
