摘要：

This chapter discusses the maximum-likelihood heavy-atom parameter refinement for multiple isomorphous replacement (MIR) and multiwavelength anomalous diffraction (MAD). The chapter describes its extension to probability distributions incorporating anomalous diffraction effects, as well as measurement error and nonisomorphism. Integrating these distributions in a whole complex plane leads to likelihood functions that can be used for heavy-atom detection and refinement and for producing phase-probability distributions. The current implementation of this formalism in the computer program statistical heavy-atom refinement and phasing (SHARP) is also described in the chapter. Likelihood functions can be used for the final phasing and calculation of Hendrickson–Lattman coefficients. Numerical tests have been performed for three types of common refinements—namely, single isomorphous replacement, multiple isomorphous replacement with anomalous scattering (MIRAS), and MAD—and the results are summarized in the chapter. A key feature of SHARP is its ability to refine lack-of-isomorphism parameters along with all the others.

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