Uncertainty Quantification and Propagation in Surrogate-based Bayesian
  Inference
Philipp Reiser Javier Enrique Aguilar Anneli Guthke Paul-Christian Bürkner
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 two detailed case
studies for both linear and nonlinear 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.