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Reasonable assumptions about the statistical properties of errors in an atomic model lead to the probability distributions for the values of structure-factor phases. These distributions contain some generally unknown parameters reflecting how large the model errors are. These parameters must be determined properly to give realistic estimates of phase errors. Maximum-likelihood-based estimates suggested by Lunin & Urzhumtsev [Acta Cryst. (1984), A40, 269-277] are good for models not subjected to refinement but underestimate the errors when being used for refined models. The R-free methodology of Brünger [Nature (London), (1992), 355, 472-474] applied to the likelihood-function calculation allows realistic phase-error estimates to be obtained for both unrefined and refined models. These estimates may be used as an additional indicator in the refinement process.
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