A computationally-tractable measure of global sensitivity for sampling-based Bayesian inference

2026-05-27

AI Summary

This work addresses the challenge of efficiently quantifying the global sensitivity of Bayesian inference to perturbations in prior or likelihood hyperparameters, particularly in high-dimensional settings where existing methods struggle. The authors propose a novel global sensitivity analysis framework based on Fisher divergence, which requires only posterior samples and evaluations of the score function to effectively measure the impact of hyperparameter perturbations on the entire posterior distribution. By introducing Fisher divergence into global sensitivity analysis for the first time, the method achieves strong theoretical rigor while substantially reducing computational cost, making it suitable for complex Bayesian models—including high-dimensional and unnormalized scenarios. Empirical results demonstrate its effectiveness in capturing the influence of perturbations on both the first- and second-order moments of the posterior across diverse applications such as generalized Bayesian inference, time series modeling, and neural simulation-based inference.

Abstract

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice. Unfortunately, existing sensitivity methods are rarely applicable in modern Bayesian workflows due to their high computational cost and poor performance in moderate to high dimensions. To address these limitations, we introduce a new approach to global sensitivity analysis based on the Fisher divergence. Our method only requires a set of samples from a reference posterior and the ability to evaluate score functions, making it broadly computationally tractable. Under mild regularity conditions, it controls changes in the whole posterior, and provides a bound on the impact of perturbations on the first two moments. We demonstrate these strengths on challenging Bayesian inference problems which are practically out of reach of existing approaches, including generalised Bayesian inference for unnormalised models, inference in Bayesian models of time series, and neural simulation-based inference.

Problem

• Bayesian inference
• global sensitivity analysis
• hyperparameter sensitivity
• computational tractability
• posterior perturbation

Innovation

• global sensitivity analysis
• Fisher divergence
• Bayesian inference
• score function
• computational tractability