Statistical inverse problems and uncertainty quantification
Statistical inverse problems refer to situations where we can get data in one domain, but our interest lies in another domain where measurements cannot be taken. This subject has a high-tech flavour and is the focus of much current research. Typical kinds of statistical inverse problems include nonparametric curve estimation like regression functions and densities. Often statistical inversion reformulates inverse problems as problems of statistical inference by means of Bayesian statistics. Uncertainty quantification is concerned with quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
