Surrogate-Based Bayesian Inference: Uncertainty Quantification and Active Learning

TL;DR

This paper reviews surrogate models in Bayesian inference, emphasizing uncertainty propagation and active learning, to unify diverse research efforts and improve practical applications in computationally intensive settings.

Contribution

It provides a comprehensive synthesis of surrogate-based Bayesian inference methods, highlighting the importance of uncertainty quantification and active learning within a unified framework.

Findings

Surrogate models effectively facilitate Bayesian inference in computationally expensive scenarios.

Propagating surrogate uncertainty improves the robustness of Bayesian analysis.

Active learning strategies enhance surrogate accuracy and efficiency.

Abstract

Surrogate models - also called emulators - are widely used to facilitate Bayesian inference in settings where computational costs preclude the use of standard posterior inference algorithms. Their deployment is now standard practice across many scientific domains. However, integrating surrogates in statistical analyses introduces unique challenges that complicate established Bayesian workflow principles. While significant progress has been made in addressing these issues, the relevant developments are scattered across several distinct research communities, with different emphases and perspective. We present a unifying review that synthesizes the literature into a coherent framework, aiming to benefit both practitioners and methods developers. We place particular emphasis on propagating surrogate uncertainty and sequentially refining emulators via active learning, two key components of a robust surrogate-based Bayesian workflow.