Journal of Applied Crystallography

Volume 39, Part 6 (December 2006)

research papers

J. Appl. Cryst. (2006). 39, 797-804 [ doi:10.1107/S0021889806035291 ]

Application of Bayesian analysis to indirect Fourier transformation in small-angle scattering

B. Vestergaard and S. Hansen

Abstract: Using Bayesian analysis for indirect Fourier transformation (IFT) of data from small-angle scattering (SAS) leads to probability distributions for parameters describing the experimental data. This quantification may provide extra information about the scattering system. The shape of the probability distribution for the maximum diameter of the scatterer may contain information about e.g. the heterogeneity of the scattering sample. The information content in the experimental data can be quantified as an `effective number of parameters' which can be determined from the data. The applicability of the Bayesian approach to IFT in SAS is demonstrated using simulated as well as experimental data.

Keywords: Bayesian analysis; indirect Fourier transformation; small-angle scattering.