Bayesian weighting for macromolecular crystallographic refinement

A simple weighting scheme for atomic refinement is discussed. The approach, called 'Bayesian weighting', is designed to be robust with respect to the bias that arises from the incomplete nature of the atomic model, which in macromolecular crystallography is typically quite serious. Bayesian weights are based on the mean-squared residual errors over shells of resolution, with centric and acentric reflections considered separately and with allowances made for experimental uncertainties. Use of Bayesian weighting is shown in test cases typical for macromolecular crystallography to improve the accuracy of the refined coordinates when compared with schemes employing unit weights or experimental variances.