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International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 18.4, p. 396
Section 18.4.3.4. Maximum likelihood
a
National Cancer Institute, Brookhaven National Laboratory, Building 725A-X9, Upton, NY 11973, USA,bStructural Biology Laboratory, Department of Chemistry, University of York, York YO10 5DD, England, and CLRC, Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, England, and cStructural Biology Laboratory, Department of Chemistry, University of York, York YO10 5DD, England |
This provides a more statistically sound alternative to least squares, especially in the early stages of refinement when the model lies far from the minimum. This approach increases the radius of convergence, takes into account experimental uncertainties, and in the final stages gives results similar to least squares, but with improved weights (Murshudov et al., 1997![[link]](/graphics/greenarr.gif)
; Bricogne, 1997). The maximum-likelihood approach has been extended to allow refinement of a full atomic anisotropic model, while retaining the use of fast Fourier algorithms (Murshudov et al., 1999). A remaining limitation is the use of the diagonal approximation, which prevents the computation of standard uncertainties of individual parameters. Algorithms that will alleviate this limitation can be foreseen, and they are expected to be implemented in the near future.
References
Bricogne, G. (1997). Maximum entropy methods and the Bayesian programme. In Proceedings of the CCP4 study weekend. Recent advances in phasing, edited by K. S. Wilson, G. Davies, A. W. Ashton & S. Bailey, pp. 159–178. Warrington: Daresbury Laboratory.Google Scholar
Murshudov, G. N., Vagin, A. A. & Dodson, E. J. (1997). Refinement of macromolecular structures by the maximum-likelihood method. Acta Cryst. D53, 240–255.Google Scholar
Murshudov, G. N., Vagin, A. A., Lebedev, A., Wilson, K. S. & Dodson, E. J. (1999). Efficient anisotropic refinement of macromolecular structures using FFT. Acta Cryst. D55, 247–255.Google Scholar
