Robust Bayesian methods using amortized simulation-based inference

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been much recent work on modified SBI approaches which are robust to misspecified likelihoods. However, less attention has been given to the issue of inappropriate prior specification, which is the focus of this work. In conventional Bayesian modelling, there will often be a wide range of prior distributions consistent with limited prior knowledge expressed by an expert. Choosing a single prior can lead to an inappropriate choice, possibly conflicting with the likelihood information. Robust Bayesian methods, where a class of priors is considered instead of a single prior, can address this issue. For each density in the prior class, a posterior can be computed, and the range of the resulting inferences is informative about posterior sensitivity to the prior imprecision. We consider density ratio classes for the prior and implement robust Bayesian SBI using amortized neural methods developed recently in the literature. We also discuss methods for checking for conflict between a density ratio class of priors and the likelihood, and sequential updating methods for examining conflict between different groups of summary statistics. The methods are illustrated for several simulated and real examples.