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 article 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.
David Nott was supported by a Singapore Ministry of Education Academic Research Fund Tier 2 grant (R-155-000-143-112). Christopher C. Drovandi was supported by an Australian Research Councils Discovery Early Career Researcher Award funding scheme (DE160100741). Kerrie Mengersen was supported by an Australian Research Council Laureate Fellowship. Michael Evans was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.