Estimates of the twinning fraction for macromolecular crystals using statistical models accounting for experimental errors.

An advanced statistical model is suggested that is designed to estimate the twinning fraction in merohedrally (or pseudo-merohedrally) twinned crystals. The model takes experimental errors of the measured intensities into account and is adapted to the accuracy of a particular X-ray experiment through the standard deviations of the reflection intensities. The theoretical probability distributions for the improved model are calculated using a Monte Carlo-type simulation procedure. The use of different statistical criteria (including likelihood) to estimate the optimal twinning-fraction value is discussed. The improved model enables better agreement of theoretical and observed cumulative distribution functions to be obtained and produces twinning-fraction estimates that are closer to the refined values in comparison to the conventional model, which disregards experimental errors. The results of the two approaches converge when applied to selected subsets of measured intensities of high accuracy.