Learning Likelihood-Free Reference Priors

Simulation modeling offers a flexible approach to constructing high-fidelity synthetic representations of complex real-world systems. However, the increased complexity of such models introduces additional complications when carrying out statistical inference procedures. This has motivated a large and growing literature on likelihood-free or simulationbased inference methods, which approximate (e.g., Bayesian) inference without assuming access to the simulator's intractable likelihood function. A hitherto neglected problem in the simulation-based Bayesian inference literature is the challenge of constructing uninformative reference priors for complex simulation models. Such priors maximise an expected Kullback-Leibler divergence from the prior to the posterior, thereby influencing posterior inferences minimally and enabling an "objective" approach to Bayesian inference that do not necessitate the incorporation of strong subjective prior beliefs. In this paper, we propose and test a selection of likelihood-free methods for learning reference priors for simulation models, using variational approximations and a variety of mutual information estimators. Our experiments demonstrate that good approximations to reference priors for simulation models are in this way attainable, providing a first step towards the development of likelihood-free objective Bayesian inference procedures.