International Tables for Crystallography

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Other refinement methods
E. Prince and D. M. Collins. International Tables for Crystallography (2006). Vol. C, ch. 8.2, pp. 689-692  [ doi:10.1107/97809553602060000610 ]

Abstract

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.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.