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Bayesian estimation of hyperparameters for indirect Fourier transformation in small‐angle scattering
Author(s) -
Hansen Steen
Publication year - 2000
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889800012930
Subject(s) - hyperparameter , transformation (genetics) , bayesian probability , fourier transform , posterior probability , computer science , mathematics , hyperparameter optimization , algorithm , statistics , artificial intelligence , mathematical analysis , chemistry , biochemistry , support vector machine , gene
Bayesian analysis is applied to the problem of estimation of hyperparameters, which are necessary for indirect Fourier transformation of small‐angle scattering data. The hyperparameters most frequently needed are the overall noise level of the experiment and the maximum dimension of the scatterer. Bayesian methods allow the posterior probability distribution for the hyperparameters to be determined, making it possible to calculate the distance distribution function of interest as the weighted mean of all possible solutions to the indirect transformation problem. Consequently no choice of hyperparameters has to be made. The applicability of the method is demonstrated using simulated as well as real experimental data.