Bayesian-calibrated global sensitivity analysis for mathematical models using generative AI

TL;DR

This paper introduces a new method using generative AI to analyze how sensitive biological models are to parameter changes, even when parameters are correlated.

Contribution

A novel Bayesian-calibrated global sensitivity analysis framework using generative models that handles parameter correlations without restrictive assumptions.

Findings

The method effectively captures parameter sensitivities in the presence of correlations in biological models.

It achieves scalability and flexibility improvements over existing sensitivity analysis techniques.

Applications to a COVID-19 and cancer immunotherapy model demonstrate its effectiveness.

Abstract

We present a generative modeling framework for global sensitivity analysis (GSA) in complex systems characterized by strong and potentially high-dimensional parameter correlations. Traditional variance-based GSA methods rely on the assumption of independent inputs, which rarely holds for Bayesian-calibrated models. While recent extensions using Rosenblatt transformations and Shapley effects theoretically address this limitation, their implementation requires accurate conditional sampling from correlated joint distributions, a task that remains challenging. Existing solutions suffer from restrictive assumptions on input dependence, which limit their applicability to complex data-driven problems. Our method addresses these challenges by reframing sensitivity analysis as a post calibration task on Bayesian posterior distributions, where parameter correlations are learned from data using generative models, eliminating restrictive dependence assumptions and ensuring data relevant sensitivity estimates. We employ autoregressive architectures to implement Rosenblatt transformations and leverage diffusion models to estimate Shapley effects. These methods impose no predefined distributional assumptions and scale efficiently with both data volume and model complexity. We demonstrate the effectiveness of our approach on two representative applications: a COVID-19 transmission model and a cancer immunotherapy model. Results show that our methods effectively captures parameter sensitivities in the presence of parameter correlations, and achieve notable gains in scalability and flexibility over existing methods.

In this research, we introduce a novel approach for conducting global sensitivity analysis in biological models using generative AI. Our method is fully compatible with Bayesian inference, which is widely used for parameter calibration of biological systems. Unlike traditional sensitivity analyses that assume independent parameters or impose simplified dependence structures, our approach performs sensitivity analysis directly on Bayesian-calibrated posterior distributions, where parameter correlations are learned from observational data. As a result, the resulting sensitivity analysis reflects realistic, data relevant parameter sensitivities rather than purely structural sensitivities of an abstract model. The proposed framework is flexible, scalable, and broadly applicable to a wide range of deterministic models calibrated through Bayesian methods. Furthermore, the generative nature of the approach paves the way for future extensions to distributional sensitivity analysis in stochastic or agent-based models, enhancing its potential for modern biological applications.

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