Bayesian Inference for Uncertainty Quantification and Inverse Problems

The predictive simulation of engineering systems increasingly rests on the synthesis of physical models and experimental data. In this context, Bayesian inference establishes a framework for quantifying the encountered uncertainties and fusing the available information. A summary and discussion of some recently emerged methods for uncertainty propagation (polynomial chaos expansions) and related MCMC-free techniques for posterior computation (spectral likelihood expansions, optimal transportation theory) is presented.