INFORMATION-GEOMETRY-BASED ROBUST BAYESIAN ANALYSIS

In this paper we introduce a novel approach for studying the influence of the choice of the prior distribution on Bayesian inference results. We define perturbed-law-based sensitivity indices (PLI) for Bayesian inference in order to provide a quantitative description of the impact of a lack of knowledge about the prior on Bayesian inference results. Based on recent work in the field of robustness analysis, these indices rely on perturbations of a reference prior, which are based on the concept of Fisher distance taken from information geometry. We also show that the proposed PLI can be reformulated as the relative variation of probabilities of rare events, which facilitates their practical computation. The proposed approach is showcased through several application examples involving Bayesian inverse problems with varying complexity. Results emphasize that the proposed approach enables the identification of parameters whose prior distribution choice has a significant impact on the inference results. Furthermore, it remains feasible in the case of Bayesian inverse problems with nonlinear forward models and possibly high-dimensional inputs, while allowing an arbitrary perturbation level for the prior.