Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference
This work solves the issue of biased and overconfident parameter estimates in surrogate-based Bayesian inference, which is incremental as it builds on existing methods to improve scalability and applicability.
The paper tackles the problem of uncertainty quantification and propagation in surrogate models for Bayesian inference, proposing a scalable framework that addresses computational limitations and demonstrates its effectiveness in linear and nonlinear real-world case studies.
Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to predictions, inference, and subsequent decision-relevant quantities. However, quantifying and then propagating the uncertainty of surrogates is usually limited to special analytic cases or is otherwise computationally very expensive. In this paper, we propose a framework enabling a scalable, Bayesian approach to surrogate modeling with thorough uncertainty quantification, propagation, and validation. Specifically, we present three methods for Bayesian inference with surrogate models given measurement data. This is a task where the propagation of surrogate uncertainty is especially relevant, because failing to account for it may lead to biased and/or overconfident estimates of the parameters of interest. We showcase our approach in three detailed case studies for linear and nonlinear real-world modeling scenarios. Uncertainty propagation in surrogate models enables more reliable and safe approximation of expensive simulators and will therefore be useful in various fields of applications.