title: Indirect Fourier transform in the context of statistical inference.
abstract: Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.
authors: Technische Universität Berlin, Stranski Laboratorium für Physikalische und Theoretische Chemie, Institut für Chemie, Strasse des 17. Juni 124, Sekr. TC7, 10623 Berlin, Germany.
authors: Michael
authors: M
authors: Muthig
authors: Technische Universität Berlin, Stranski Laboratorium für Physikalische und Theoretische Chemie, Institut für Chemie, Strasse des 17. Juni 124, Sekr. TC7, 10623 Berlin, Germany.
authors: Sylvain
authors: S
authors: Prévost
authors: Technische Universität Berlin, Elektronik und medizinische Signalverabeitung, Sekr. EN3, Einsteinufer 17, 10587 Berlin, Germany.
authors: Reinhold
authors: R
authors: Orglmeister
authors: Technische Universität Berlin, Stranski Laboratorium für Physikalische und Theoretische Chemie, Institut für Chemie, Strasse des 17. Juni 124, Sekr. TC7, 10623 Berlin, Germany.
authors: Michael
authors: M
authors: Gradzielski
keywords: Bayesian statistical inference; frequentist statistical inference; indirect Fourier transform (IFT); model selection