Stochastic Spectral Methods for Linear Bayesian Inference

Simulation-based control of dynamic systems is of key importance for many areas of science and industry. To ensure the predictive capabilities, simulation models used for predicting control responses have to be calibrated to available observations. Bayesian approaches to make inference from data on unobservable quantities are used because of their consistent, inherent treatment of diverse sources of uncertainties. Spectral approaches to uncertainty quantification have become popular over the last years. However, their combination with Bayesian inference usually employs expensive probabilistic sampling methods. In this work, a family of linear Bayesian approaches is presented which directly results in a representation of the posterior. A specific implementation is discussed which overcomes some of the difficulties that remained unsolved in related approaches. All implementation details are given, and the applicability is demonstrated on some linear and non-linear numerical examples.