Chapter 8.2 Other refinement methods
Mathematical, physical and chemical tables
First Online Edition (2006)
Part 8. Refinement of structural parameters
Published Online: 1 JAN 2006
© International Union of Crystallography 2006
International Tables for Crystallography
How to Cite
Prince, E. and Collins, D. M. 2006. Other refinement methods. International Tables for Crystallography. C:8:8.2:689–692.
- Published Online: 1 JAN 2006
Least squares is a powerful data fitting method when the distribution of statistical fluctuation in the data is approximately normal, or Gaussian, but it can perform poorly if the distribution function has longer tails than a Gaussian distribution. Chapter 8.2 discusses several procedures that work better than least squares if the normality condition is not satisfied. Maximum likelihood methods, which are identical to least squares for a normal distribution, can be designed to be optimum for any distribution. Other methods are robust, because they work well over a broad range of distributions, and resistant, because they are insensitive to the presence in the data of points that disagree with the model. Maximum entropy methods are particularly useful when there are insufficient data.
- entropy maximization;
- maximum‐likelihood methods;
- robust/resistant methods