Andrew Gerard Roberts

arXiv2026

Surrogate-Based Bayesian Inference: Uncertainty Quantification and Active Learning

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.

stat.ME↗

arXiv2026

Propagating Surrogate Uncertainty in Bayesian Inverse Problems

Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential to acknowledge the surrogate approximation by propagating its uncertainty. At present, a variety of distinct uncertainty propagation methods have been suggested, with little understanding of how they vary. To fill this gap, we propose a mixture distribution termed the expected posterior (EP) as a general baseline for uncertainty-aware posterior approximation, justified by decision theoretic and modular Bayesian inference arguments. We then investigate the expected unnormalized posterior (EUP), a popular heuristic alternative, analyzing when it may deviate from the EP baseline. Our results show that this heuristic can break down when the surrogate uncertainty is highly non-uniform over the design space, as can be the case when the log-likelihood is emulated by a Gaussian process. Finally, we present the random kernel preconditioned Crank-Nicolson (RKpCN) algorithm, an approximate Markov chain Monte Carlo scheme that provides practical EP approximation in the challenging setting involving infinite-dimensional Gaussian process surrogates.

stat.ME↗