CRC 1294/1: Nonlinear Statistical Inverse Problems With Random Observations (SP A04)

The project deals with nonlinear statistical inverse problems; the goal is to estimate from random observations the functional relation between observable covariates and intrinsic (unobservable) parameters of a system whose output is observed. The system itself is known (up to the intrinsic parameters) through a specific model, e.g. a differential equation. The main objective is to design suitable non-parametric estimators using a reproducing kernel ansatz, i.e., nonlinear regularized maximum likelihood estimators, and to analyze their theoretical performance. Mechanistic modelling approaches from pharmacokinetics serve as a specific application. Questions relating to efficient computation of the estimate as well as associated quantification of uncertainty will be addressed.