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Estimating the difference between structure-factor amplitudes using multivariate Bayesian inference

Journal article
Authors Gergely Katona
Maria-Jose Garcia-Bonete
Ida Lundholm
Published in Acta Crystallographica a-Foundation and Advances
Volume 72
Pages 406-411
ISSN 2053-2733
Publication year 2016
Published at Department of Chemistry and Molecular Biology
Pages 406-411
Language en
Keywords experimental phasing, self-referencing, Bayesian model, time-resolved crystallography, Markov chain Monte Carlo algorithm, crystallography, protein, Chemistry, Crystallography
Subject categories Chemical Sciences, Statistics, computer and systems science


In experimental research referencing two or more measurements to one another is a powerful tool to reduce the effect of systematic errors between different sets of measurements. The interesting quantity is usually derived from two measurements on the same sample under different conditions. While an elaborate experimental design is essential for improving the estimate, the data analysis should also maximally exploit the covariance between the measurements. In X-ray crystallography the difference between structure-factor amplitudes carries important information to solve experimental phasing problems or to determine time-dependent structural changes in pump-probe experiments. Here a multivariate Bayesian method was used to analyse intensity measurement pairs to determine their underlying structure-factor amplitudes and their differences. The posterior distribution of the model parameter was approximated with a Markov chain Monte Carlo algorithm. The described merging method is shown to be especially advantageous when systematic and random errors result in recording negative intensity measurements.

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