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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.<\/jats:p>","DOI":"10.1007\/s11222-025-10597-8","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T13:04:49Z","timestamp":1741871089000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Uncertainty quantification and propagation in surrogate-based Bayesian inference"],"prefix":"10.1007","volume":"35","author":[{"given":"Philipp","family":"Reiser","sequence":"first","affiliation":[]},{"given":"Javier Enrique","family":"Aguilar","sequence":"additional","affiliation":[]},{"given":"Anneli","family":"Guthke","sequence":"additional","affiliation":[]},{"given":"Paul-Christian","family":"B\u00fcrkner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"issue":"1","key":"10597_CR1","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TCBB.2018.2843339","volume":"17","author":"K Alden","year":"2020","unstructured":"Alden, K., Cosgrove, J., Coles, M., Timmis, J.: Using emulation to engineer and understand simulations of biological systems. 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