Keywords:
phases errors, likelihood function, ML-estimates, MLL-estimates,
R-free.
The phases quality estimates derived
from the maximization of the likelihood function (ML-estimates)
were shown to be superior in comparison with other ones when dealing
with phases calculated from an atomic model with independent coordinate
errors [1] and were incorporated into wide-spread program SIGMAA.
Nevertheless, it was found that ML-estimates have essential bias
and overestimate the model quality when used for the atomic models
refined in the reciprocal space [1, 2, 3].
The use of marginal likelihood function
calculated in the framework of R-free-approach on the base of
the test reflections only [4] allows one to obtain more reliable
estimates (MML-estimates) both for unrefined and refined models
[3, 5]. At the same time MML-estimates being derived on the base
of a relatively small number of observations are prone to large
statistical deviations from the mean. A simple smoothing procedure
applied to structure factor distribution parameters allows one
to reduce the statistical spread in the estimates significantly.
[1] Read, R. J. (1986). Acta Cryst. A42, 140-149.
[2] Lunin, V. Yu. & Urzhumtsev, A. G. (1984). Acta Cryst. A40, 265-277.
[3] Lunin, V. Yu. & Skovoroda, T. P. (1995). Acta Cryst. A51, 880-887.
[4] Brnger, A. T. (1992). Nature (London), 355, 472-474.
[5] Urzhumtsev, A. G., Skovoroda T. P. & Lunin V. Yu. (1996). J. Appl. Cryst. 29, 741-744.