Abstract
The Maximum-Entropy method is applied to the determination of the distance distribution function in small-angle scattering. Alternative methods for this purpose suffer from problems caused by their ad hoc nature, but the Maximum-Entropy method has a well established theoretical foundation offering several advantages. Examples are given using simulated as well as experimental data. It is demonstrated that the “best” (most likely) choice of parameters as e.g. the noise level, the model or the regularisation method in general can be found from the evidence in a Bayesian framework.
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References
Arnott S.,D.W.L. Hukins, Dover S.D.:1972, ‘Optimized Parameters for RNA Double Helices’, Biochem. Biophys. Res. Commun. 48, 1392–1399.
Brunel Ch.,Romby P.,Westhof E., Ehresmann Ch., Ehresmann B.: 1991, ‘Three-dimensional Model of Escherichia coli Ribosomal 5S RNA as Deduced from Structure Probing in Solution and Computer Modelling’, J Mol. Biol.221, 293–308.
Bryan, R.K.: 1990, ‘Maximum entropy analysis of oversampled data problems’, Eur. Biophys. J18, 165–174.
Charter, M.K., and Gull, S.F.: 1991, ‘Maximum Entropy and Drug Absorption’,J. Pharmacokin. Biopharm19, 497–520.
Damaschun, G., Müller, J.J., Bielka, H.: 1979, ‘Scattering Studies of Ribosomes and Ribosomal Components’ Methods in Enzymology59, 706–750.
Potton, J. A., Daniell, G. J. & Rainford, B. D.: 1988a, ‘Particle Size Distributions from SANS Using th Maximum Entropy Method’, J. Appl. Cryst.21, 663–668.
Potton, J. A., Daniell, G. J. & Rainford, B. D.: 1988b, ‘A New Method for the Determination of Particle Size Distributions from Small-Angle Neutron Scattering’, J. Appl. Cryst21, 891–897.
Hansen, S. & Pedersen, J. S.: 1991, ‘A Comparison of Three Different Methods for Analysing Small-Angle Scattering Data’, J. Appl. Cryst24, 541–548.
Hansen, S. & Wilkins, S. W.: 1994, ‘On uncertainty in maximum-entropy maps and the generalization of ’classic MaxEnt”, Acta CrystA50, 547–550.
Glatter, O.: 1977, ‘A New Method for the Evaluation of Small-Angle Scattering Data’,J. Appl. Cryst10, 415–421.
Glatter, O.: 1982, In Small Angle X-ray Scattering, edited by O. Glatter and O. Kratky. Academic Press, London
Gull, S.F.: 1989, ‘Developments in Maximum Entropy Data Analysis’, in Maximum-Entropy and Bayesian Methods, edited by J. Skilling, pp. 53–71. Dordrecht: Kluwer Academic Publishers.
MacKay, D.J.C.: 1992, ’Bayesian Interpolation’, in Maximum Entropy and Bayesian Methods, Seattle 1991, edited by C.R.Smith et al, pp. 39–66. Kluwer Academic Publishers, Netherlands.
May, R. P. & Nowotny, V. (1989). ‘Distance Information Derived from Neutron Low-Q Scattering’ J. Appl. Cryst22, 231–237.
Moore, P. B. (1980). ’Small-Angle Scattering. Information Content and Error Analysis’ J. Appl. Cryst13, 168–175.
Morrison, J. D., Corcoran, J. D. & Lewis, K. E.: 1992, ‘The Determination of Particle Size Distributions in Small-Angle Scattering Using the Maximum-Entropy Method’, J. Appl. Cryst25, 504–513.
Müller, J.J., &Zalkova, T.N., Zirwe, D., Misselwits, R., Gast K., Seryuk I.N., Welfle H., Damaschun, G.: 1986,‘Comparison of the structure of ribosomal 5S RNA from E. coli and from rat liver using X-ray scattering and dynamic light scattering’, Eur.Biophys. J. 13 301–307.
Müller, J.J. & Hansen, S.: 1994,‘A Study of High-Resolution X-ray Scattering Data Evaluation by the Maximum-Entropy Method’, J. Appl. Cryst. 27 257–270.
Skiling, J.: 1988, ‘ The Axioms of Maximum Entropy’Maximum-Entropy and Bayesian Method in Science and Engineering (Vol 1), edited by G.J. Erickson and C. Ray Smith, pp. 173–187. Kluwer Academic Publishers, Dordrecht.
Skilling, J.: 1988, ‘Classical Maximum Entropy’, in Maximum- Entropy and Bayesian Methods, edited by J. Skilling, pp. 42–52. Kluwer Academic Publishers, Dordrecht.
Skilling, J.: 1991, ‘On parameter estimation and quantified MaxEnt’ in Maximum-Entropy and Bayesian Methods, edited by Grandy and Schick, pp. 267–273. Kluwer Academic Publisher, Dordrecht.
Steenstrup, s. & Hansen, S.: 1994,’The Maximum-Entropy Method without the Positivity Constraint ‘ Applications to the Determination of the Distance-Distribution Function in Small-Angel Scattering’, J. Appl. Cryst. 25, 574–580.
Svergun, D. I.: 1992,‘Determination of the Regularization Parameter in Indirect-Transform Methods Using Perceptual Criteria’, J Appl. Cryst. 25, 495–503.
Svergun, D.I., Semenyuk, A.V & Feigin, L.A.: 1988,‘Small-Angle Scattering-Data Treatment Method’, Acta Cryst. A44, 244–250.
Tikhonov, A.N. & Arsenin, V.Ya.: 1977, in Solution of Il-Posed Problems, New York: Wiley.
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Hansen, S., Müller, J.J. (1996). The Maximum-Entropy Method in Small-Angle Scattering. In: Skilling, J., Sibisi, S. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 70. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0107-0_8
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DOI: https://doi.org/10.1007/978-94-009-0107-0_8
Publisher Name: Springer, Dordrecht
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