**The
Maximum Entropy Method: ** ** **Traditional direct methods have
proved to be immensely successful when applied to single crystals where the
diffraction data are complete and have atomic resolution (*i.e.* around
1.1Å), but this leaves whole classes of important problems which are inaccessible
to such techniques *i.e*. electron diffraction data, powders, proteins
and surfaces.

A new method, the maximum entropy (ME) formalism, has the potential to tackle these problems, and has been developed as a practical technique for solving crystal structures. Based on information theory and using Bayesian statistics, it builds electron density through constrained entropy maximisation.

Phasing
tree in the maximum entropy method |

**References
for Maximum Entropy Methods:**

- 'A Multisolution Phase
Determination Method in X-ray Crystallography', C.Bannister, G.Bricogne &
C.J.Gilmore, in
*Bayesian Methods and Maximum Entropy,*Ed. J.Skilling, Kluwer, (1989), 225-232. - 'A Multisolution Method
of Phase Determination by Combined Maximisation of Entropy and Likelihood.
I: Theory, Algorithms and Strategy', G.Bricogne & C.J.Gilmore,
*Acta Cryst,*(1990),**A46,**284-297.'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. II: Applications to Small Molecules', C.J.Gilmore, G.Bricogne & C. Bannister,*Acta Cryst.*(1990),**A46,**297-308. - ‘Maximum Entropy, Likelihood
and the Phase Problem in Single Crystal and Powder Diffraction' C.J. Gilmore
& G.Bricogne in
*Crystallographic Computing 5,*Ed. D.Moras Oxford University Press, (1991), 298-307. - 'A Multisolution Method
of Phase Determination by Combined Maximisation of Entropy and Likelihood.
VI Automatic Likelihood Analysis via the Student t-test, with an application
to the Powder Structure of Magnesium Boron Nitride', K.Shankland, C.J. Gilmore,
G.Bricogne, & H.Hashizume,
*Acta Cryst.*(1993),**A49**, 493-501. - 'Applications of the
Maximum Entropy Method to Powder Diffraction and Electron Crystallography'
*,*C.J.Gilmore, K.Shankland & G.Bricogne*Proc. Roy. Soc. Series A,*(1993),**442,**97-111. - 'Maximum Entropy, Likelihood
Ranking and the Phase Problem for Single Crystal, Powder Diffraction and Electron
Microscopy' C.J.Gilmore in
*Crystallographic Computing 6: A Window on Modern Crystallography*, Ed. H. Flack, Oxford University Press, (1993), 25-46. - 'The MICE Computer Program,
and its application to Direct Phase Determination for Powders, Electron Diffraction
and Macromolecules', C.J.Gilmore & W.Nicholson
*Trans. Amer. Cryst. Association.*(1994),**30**, 15-27. - 'Maximum Entropy and
Bayesian Statistics in Crystallography' C.J.Gilmore,
*Acta Cryst.*(1996),**A52**, 561-589 - 'MICE Computer Program'
C.J.Gilmore & G.Bricogne
*Methods in Enzymology*(1997),**277,**65-78. - 'An Introduction to
Maximum Entropy in Action' C.J.Gilmore in
*Electron Crystallography*, Ed. S.Fortier, Kluwer (1998), 109-117. - 'Structure Determination
using Maximum Entropy and Likelihood' C.J.Gilmore in
*Electron Crystallography*, Ed. D.L.Dorset, Kluwer (1997), 295-304. - 'Developments in Maximum
Entropy and Likelihood' C.J.Gilmore
*in Direct Methods in Macromolecular Crystallography,*Ed. S.Fortier, Kluwer, (1998), 455-462. - 'A Multisolution Method
of Phase Determination by Combined Maximisation of Entropy and Likelihood.
VI The Use of Error-Correcting Codes as a Source of Phase Permutation and
their Application to the Phase Problem in Powder, Electron and Macromolecular
Crystallography’
*Acta Cryst.*(1998),**A55,**70-83. - 'Direct Determination
of the Modulated Lamellar "Ripple" Phase of Hydrated Lecithin' D.L.Dorset
& C.J.Gilmore
*Z. Krist*. (1998),**213**, 432-435.