Chapter 15.2 Model phases: probabilities, bias and maps

Crystallography of biological macromolecules

First Online Edition (2006)

Part 15. Density modification and phase combination

  1. R. J. Read

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000688

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Read, R. J. 2006. Model phases: probabilities, bias and maps. International Tables for Crystallography. F:15:15.2:325–331.

Author Information

  1. Department of Haematology, University of Cambridge, Wellcome Trust Centre for Molecular Mechanisms in Disease, CIMR, Wellcome Trust/MRC Building, Hills Road, Cambridge CB2 2XY, England

Publication History

  1. Published Online: 1 JAN 2006


The optimal use of model phase information requires an estimate of its reliability, specifically the probability that various values of the phase angle are true. This chapter covers the importance of phase in model bias; structure-factor probability relationships; figure-of-merit weighting for model phases; map coefficients to reduce model bias; difference-map coefficients; refinement bias; and maximium-likelihood structure refinement.


  • Parseval’s theorem;
  • Sim distribution;
  • Wilson distribution;
  • coordinate errors;
  • figure-of-merit weighting for model phases;
  • maximum likelihood;
  • model bias;
  • model phases;
  • phase combination;
  • refinement;
  • structure-factor probability distributions