Probability calculus for quantitative HREM.Part II: Entropy and likelihood concepts

The technique of extracting atomic coordinates from HREM images by R-factor refinement via iterative simulation and global optimisation is described in the context of probability density estimations for unknown parameters. In the second part of this two-part paper we discuss in comparison maximum likelihood and maximum entropy techniques with respect to their suitability of application within HREM. We outline practical difficulties of likelihood estimation and present a synthesis of two point-cloud techniques as a recommendable solution. This R-factor refinement with independent Monte-Carlo error calibration is a highly versatile method which allows adaptation to the special needs of HREM. Unlike simple text-book estimation methods, there is no requirement here on the noise being additive, uncorrelated, or Gaussian. It also becomes possible to account for a subset of systematic errors.