For partial differential equations with random coefficients we investigate the sensitivity of the distribution of the random solution with respect to perturbations in the input distribution for the unknown data. We prove a local Lipschitz continuity with respect to total variation as well as Wasserstein distance and extend our sensitivity analysis also to quantities of interest of the solution as well as risk functionals applied to such quantities. Here, we provide a novel result for the sensitivity of coherent risk functionals with respect to the underlying probability distribution.
Besides these sensitivity results for the propagation of uncertainty, we also investigate the inverse problem, i. e., Bayesian inference for the unknown coefficients given noisy observations of the solution. Although well-posedness of Bayesian inverse problems is well-known, we extend the local Lipschitz stability of the posterior to pertubations of the prior. Again we consider stability in the Wasserstein distance as well as with respect to several other common metrics for probability measures. However, our explicit bounds indicate a growing sensitivity of Bayesian inference for increasingly informative observational data.
invited by Han Cheng Lie
***Due to the current situation concerning the pandemic the seminar will be held online. Please contact sebastian.reich[at]uni-potsdam.de to receive the zoom link.***