A likelihood-based approach to density modification for macromolecular crystallography is presented. The approach can be applied in many cases where some information is available about the electron density at various points in the unit cell. The most important aspect of the method consists of likelihood functions that represent the probability that a particular value of electron density is consistent with prior expectations for the electron density at that point in the unit cell. Such likelihood functions are combined with likelihood functions based on experiment and with any prior knowledge about structure factors to form a combined likelihood function for each structure factor. An approach for maximizing the combined likelihood function that is simple and rapid is developed.
Thomas C. Terwilliger,
"Maximum-likelihood density modification for x-ray crystallography", Proc. SPIE 4123, Image Reconstruction from Incomplete Data, (16 November 2000); doi: 10.1117/12.409275; https://doi.org/10.1117/12.409275