Bayesian correlated MAD phasing.

A Bayesian treatment for phase calculation in the multiwavelength anomalous diffraction (MAD) technique is presented. This approach explicitly treats effects of errors correlated among measurements at different wavelengths and between Bijvoet pairs. The resulting method, which is called Bayesian correlated MAD phasing, gives proper statistical consideration to all data and does not give special treatment to data from a particular wavelength. Results obtained using Bayesian correlated MAD phasing and two other strategies on both a model test case and on data obtained in two actual MAD experiments are compared. Although all procedures performed well when the completeness of the data was high, it is shown that Bayesian correlated MAD phasing is more robust with respect to incompleteness of data than the other methods are. At 60% completeness the improvement over other methods for the examples given was nearly 50% in the correlation coefficients, and made a substantial difference in the interpretability of an electron-density map.