Open AccessMaximum‐likelihood density modification
Author(s) -
Terwilliger Thomas C.
Publication year - 2000
Publication title -
acta crystallographica section d
Language(s) - English
Resource type - Journals
ISSN - 1399-0047
DOI - 10.1107/s0907444900005072
Subject(s) - flattening , likelihood function , likelihood ratio test , mathematics , probability density function , statistics , maximum likelihood , statistical physics , computer science , algorithm , materials science , physics , composite material
A likelihood‐based approach to density modification is developed that can be applied to a wide variety of cases where some information about the electron density at various points in the unit cell is available. The key to the approach consists of developing 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. These likelihood functions are then combined with likelihood functions based on experimental observations and with others containing any prior knowledge about structure factors to form a combined likelihood function for each structure factor. A simple and general approach to maximizing the combined likelihood function is developed. It is found that this likelihood‐based approach yields greater phase improvement in model and real test cases than either conventional solvent flattening and histogram matching or a recent reciprocal‐space solvent‐flattening procedure [Terwilliger (1999), Acta Cryst. D 55 , 1863–1871].