Other refinement methods

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. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.