Nicolai Bissantz, Ruhr-Universität Bochum, Bochum, Germany
We discuss statistical inference for inverse problems based on two exemplary applications. In the first part we consider the estimation of transmembrane currents through the E.coli-SecYEG-pore. Here, the statistical model is a density deconvolution problem. We present uniform confidence bands for the reconstructed density and a method for testing for the number of modes in the underlying density of interest. Application of these methods to data from a SecYEG experiment indicates the presence of single- and multiple currents through the pore. The second part of the talk is considered with gel electrophoresis of genetically engineered neuronal receptor subunits. Here the statistical model for the data belongs to a certain class of inverse regression models, for which the determination of uniform confidence bands on the reconstructed distribution of molecular masses is discussed.