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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. 16.2, p. 348
Section 16.2.3.5. Connection with the saddlepoint method
aLaboratory of Molecular Biology, Medical Research Council, Cambridge CB2 2QH, England |
The saddlepoint method constitutes an alternative approach to the problem of evaluating the joint probability ![[{\cal P}({\bf F^{*}})]](/teximages/fach16o2/fach16o2fi61.svg)
of structure factors when some of the moduli in ![[{\bf F^{*}}]](/teximages/fach16o2/fach16o2fi44.svg)
are large. It is shown in §5 of Bricogne (1984)![[link]](/graphics/greenarr.gif)
, and in more detail in Section 1.3.4.5.2.2
of Chapter 1.3 of IT B (Bricogne, 2001), that there is complete equivalence between the maximum-entropy approach to the phase problem and the classical probabilistic approach by the method of joint distributions, provided the latter is enhanced by the adoption of the saddlepoint approximation.
References
Bricogne, G. (1984). Maximum entropy and the foundations of direct methods. Acta Cryst. A40, 410–445.Google Scholar
Bricogne, G. (2001). Fourier transforms in crystallography: theory, algorithms and applications. In International tables for crystallography, Vol. B. Reciprocal space, edited by U. Shmueli, 2nd ed., ch. 1.3. Dordrecht: Kluwer Academic Publishers.Google Scholar
