Mini-workshop: Statistical Methods for Inverse Problems

Nonlinear methods for inverse statistical problems

In the uncertainty treatment framework considered in this paper, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution the dispersion of which is independent of the sample size since intrinsic variability is at stake based on observation of some model outputs. More...

Iterative Inversion Methods for Statistical Inverse Problems

In this paper we discuss general regularization estimators. This class includes Tikhonov type and spectral cut-off estimators as well as iterative methods, such as ν-methods and the Landweber iteration. The latter estimators achieve the same (optimal) convergence rates as spectral cut-off, but do not require explicit spectral information on the operator and are often much faster to compute than...

Mini Workshop on Bayesian Inverse Problems and Imaging

Filter Based Methods For Statistical Linear Inverse Problems

Ill-posed inverse problems are ubiquitous in applications. Understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system. This opens up the possibility of using a range of oth...

Statistical inference for inverse problems

In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima...