Section 25.2.1.6.2.2. Approximate-likelihood method

This variation, also available in PHASIT, is similar to the classical phase refinement described above, except that instead of using only a single value for the protein phase φ during the calculation of , all possible values are considered, with each contribution weighted by the corresponding protein phase probability (Otwinowski, 1991). One minimizes with respect to the desired parameters for isomorphous-replacement data, where is the protein phase probability and the inner summation is over all allowed protein phase values, stepped in intervals of 5° (or 180° for centric reflections). For anomalous-scattering data, a similar modification is made to equation (25.2.1.14). The weights may be as in the classical phase refinement case or unity. Since each contribution is weighted by its phase probability regardless, there is no need to use a high figure-of-merit cutoff, as was done earlier. In fact, very good results are usually obtained using unit weights for (that is, only the probability weighting) and a figure-of-merit cutoff of around 0.2 for inclusion of reflections in the summations. This variation has been found to increase stability in the refinement and works considerably better than conventional phase refinement when the phase probability distributions are strongly multimodal. Parameter refinement and phasing iterations proceed as described earlier. The combination of probability weighting during refinement with probability weighting during standard error estimation enables the key features of maximum-likelihood refinement to be carried out, although only approximately.