Local sensitivity analysis for Bayesian inverse problems
It provides a theoretical framework for efficient uncertainty quantification in Bayesian inverse problems, which is incremental as it extends existing methods.
The paper extends local sensitivity analysis to Bayesian inverse problems, enabling efficient approximation of posterior moments via asymptotic expansions under smoothness assumptions.
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the posterior distribution can be approximated efficiently by asymptotic expansions. This is under the assumption that the measurement operators and prediction functions are sufficiently smooth and their corresponding stochastic moments with respect to the prior distribution exist. Numerical experiments are presented to the illustrate the theoretical results.