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In SHELXL. a refinement program sometimes used by small molecule crystallographers, all Fourier map for at least the last 20 years were weighted by Ic^2/(Ic^2+sigma^2(I)), where Ic is the calculated squared structure factor and sigma(I) is the square root of 1/w. w is the weight assigned to a reflection in the refinement (e.g. w=1/(sig(I)^2+(gI)^2), where sig(I) is the esd of the measured intensity I and g is a small constant. This purely empirical scheme appears to result in a significant reduction in the noise level of the map, at least for typical small molecule structures. Such schemes have been called 'maximum likelihood by intuition', a proper maximum likelihood treatment taking the esds of the intensities into account would of course do much better. George On 05/23/2012 06:59 PM, Dale Tronrud wrote: > On 05/23/12 08:06, Nicholas M Glykos wrote: >> Hi Ed, >> >> >>> I may be wrong here (and please by all means correct me), but I think >>> it's not entirely true that experimental errors are not used in modern >>> map calculation algorithm. At the very least, the 2mFo-DFc maps are >>> calibrated to the model error (which can be ideologically seen as the >>> "error of experiment" if you include model inaccuracies into that). >> This is an amplitude modification. It does not change the fact that the >> sigmas are not being used in the inversion procedure [and also does not >> change the (non) treatment of missing data]. A more direct and relevant >> example to discuss (with respect to Francisco's question) would be the >> calculation of a Patterson synthesis (where the phases are known and >> fixed). >> >> >>> I have not done extensive (or any for that matter) testing, but my >>> evidence-devoid gut feeling is that maps not using experimental errors >>> (which in REFAMC can be done either via gui button or by excluding SIGFP >>> from LABIN in a script) will for a practicing crystallographer be >>> essentially indistinguishable. >> It seems that although you are not doubting the importance of maximum >> likelihood for refinement, you do seem to doubt the importance of closely >> related probabilistic methods (such as maximum entropy methods) for map >> calculation. I think you can't have it both ways ... :-) >> >> >> >>> The reason for this is that "model errors" as estimated by various >>> maximum likelihood algorithms tend to exceed experimental errors. It >>> may be that these estimates are inflated (heretical thought but when you >>> think about it uniform inflation of the SIGMA_wc may have only >>> proportional impact on the log-likelihood or even less so when they >>> correlate with experimental errors). Or it may be that the experimental >>> errors are underestimated (another heretical thought). >> My experience from comparing conventional (FFT-based) and maximum-entropy- >> related maps is that the main source of differences between the two maps >> has more to do with missing data (especially low resolution overloaded >> reflections) and putative outliers (for difference Patterson maps), but in >> certain cases (with very accurate or inaccurate data) standard deviations >> do matter. > In a continuation of this torturous diversion from the original question... > > Since your concern is not how the sigma(Fo) plays out in refinement but > how uncertainties are dealt with in the map calculation itself (where an > FFT calculates the most probable density values and maximum entropy would > calculate the "best", or centroid, density values) I believe the most > relevant measure of the uncertainty of the Fourier coefficients would be > sigma(2mFo-DFc). This would be estimated from a complex calculation of > sigma(sigmaA), sigma(Fo), sigma(Fc) and sigma(Phic). I expect that the > contribution of sigma(Fo) would be one of the smallest contributors to this > calculation, as long as Fo is "observed". I wouldn't expect the loss of > sigma(Fo) to be catastrophic. > > Wouldn't sigma(sigmaA) be the largest component since sigmaA is a function > of resolution and based only on the test set? > > Dale Tronrud > > >> >> All the best, >> Nicholas >> >> -- Prof. George M. Sheldrick FRS Dept. Structural Chemistry, University of Goettingen, Tammannstr. 4, D37077 Goettingen, Germany Tel. +49-551-39-3021 or -3068 Fax. +49-551-39-22582