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
