On 11/02/12 02:52 PM, Bryan Lepore wrote: > did you ever get a response on this? it is interesting but nobody > posted publicly. > > -Bryan >
Dear Bryan, so far no one replied ... so please find my answer below. If someone disagrees, please post. None of the methods I have described are appropriate. If the negative Bijvoet mates and the positive Bijvoet mates have been merged separately to one intensity value for each (i.e. I+ or I-) plus the associated standard deviation (sigI+ or sigI-), any weighted method to calculate the mean will bias the intensity to either the I+ or the I-. Therefore the only appropriate method is to use the unweighted mean: Imean = 0.5*( I+ + I- ) sigImean = 0.5 * sqrt( sigI+^2 + sigI-^2 ) The only CCP4 program I found that actually does this is mtzMADmod. This method also has the advantage that the original intensity values of I+ and I- can be reconstructed from the mean and the anomalous difference (albeit with the loss of the original standard deviations). Method 1 (scalepack2mtz) should not be used. The resulting value is not the best estimate (maximum likelihood) Method 2 (in book by B. Rupp) gives the maximum likelihood average in case that the reflections are equivalent and is thus appropriate for the merging of the negative (or positive) set of Bijvoet mates, centric reflections (where the anomalous differences are zero) or in the case of an non-anomalous dataset the merging of symmetry equivalent reflections. Method 3 gives a more realistic sigma value in the case that the individual intensity values are far apart and their individual standard deviations are small. Consider the example I have posted: I+: 23841.50 sigI+: 634.01 I-: 9628.57, sigI-: 264.75 Method 2: Imean=11738.95, sigIMean=244.31 Method 3: Imean=11738.95, sigIMean=7106.47 If the I+ and I- values above actually were symmetry equivalent reflections in an non-anomalous dataset, the sigImean from method 2 is ridiculously small and method 3 gives a far more realistic value. If method 3 is the best mathematical solution to this problem I am not able to judge and I have to trust the statistician (or programmer) who implemented this solution. Cheers, Markus On 10/02/12 01:47 PM, Markus Meier wrote: > Dear all, > I have a anomalous dataset, processed in HKL2000. Scalepack outputs a > file containing the separately merged sets of the Friedel pairs I- and > I+ and their standard deviations sigI+ and sigI-. Scalepack does not > output the averaged intensities (Imean) and the standard deviations > (sigIMean). > > The CCP4 program truncate that I use to convert the intensities to > amplitudes requires Imean, I- and I+ and the respective standard > deviations in its input file. > > I have now found at least three different methods to generate the > averaged intensities from the Friedel pairs: > > 1) scalepack2mtz > > uses standard deviations for the weights: > weights w = 1/sigI > > Imean = (w+*I+ + w-*I- ) / (w+ + w-) > sigImean = 1 / (w+ + w-) > > 2) Method described in Biomolecular crystallography by Bernhard Rupp, p. > 332/333 > to average symmetry equivalent reflections > > uses variances for the weights: > weight w = 1/sigI^2 > > Imean = (w+*I+ + w-*I- ) / (w+ + w-) > sigImean = 1 / sqrt(w+ + w-) > > 3) Method used in cctbx > function miller.set.average_bijvoet_mates() that calls generic > merge.merge_equivalent_obs(): > > same as methods 2, except that > > sigImean is the larger of either > a) sigImean = 1 / sqrt(w+ + w-) > or > b) sigImean = sqrt( wvariance ) > > where wvariance = > (w+ + w-) / [ (w+ + w-)^2 - (w+^2 + w-^2) ] * > [ w+*(F+ - Imean)^2 + w-*(F- - Imean)^2 ] > > What are the advantages and disadvantages of each method? Should method > 1 be used at all? > > Some example from my dataset: > Reflection (1, 1, 0), space group P3 2 1 > > I+: 23841.50 sigI+: 634.01 I-: 9628.57, sigI-: 264.75 > Method 1: Imean=13815.32, sigImean=186.76 > Method 2: Imean=11738.95, sigIMean=244.31 > Method 3: Imean=11738.95, sigIMean=7106.47 > > Thanks a lot! > > Cheers, > Markus -- Markus Meier, Ph.D. University of Manitoba Department of Chemistry 144 Dysart Road Winnipeg, MB, R3T 2N2, Canada Phone: +1 204 474 7172 Fax: +1 204 474 7608 E-mail: me...@cc.umanitoba.ca
