Bayesian estimation of hyperparameters for indirect Fourier transformation in small-angle scattering
نویسنده
چکیده
Author(s) of this paper may load this reprint on their own web site provided that this cover page is retained. Republication of this article or its storage in electronic databases or the like is not permitted without prior permission in writing from the IUCr. 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.
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