Simple algorithm for a maximum-likelihood SAD function

Recently, the multivariate complex normal distribution has been used to develop a maximum-likelihood probability function for single-wavelength anomalous diffraction phasing and refinement of heavy-atom parameters [Pannu & Read ( 2004), Acta Cryst. D60, 22 - 27]. The function accounts explicitly for the correlations between the observed and calculated Friedel mates and their errors. However, the method of derivation of the equation described by Pannu & Read ( 2004) leads to a complicated likelihood expression that suffers from a number of algorithmic limitations. Here, an alternative derivation of the P-SAD function is described that leads to simplified algorithmic requirements and that allows an intuitive understanding of the expression.