Here we are I presume only worried about strong reflections lost behind
an ice ring. At least that is where the discussion began.
Isnt the best approach t this problem to use integration software which
attempts to give a measurement, albeit with a high error estimate?
The discussion has strayed into what to do with incomplete data sets..
In these cases there might be something to learn from the Free Lunch
ideas used in ACORN and SHELX and other programs - set the missing
reflections to E=1, and normalise them properly to an appropriate amplitude.
Eleanor
On 10/11/2011 08:33 PM, Garib N Murshudov wrote:
In the limit yes. however limit is when we do not have solution, i.e. when model errors are very large. In
the limit map coefficients will be 0 even for 2mFo-DFc maps. In refinement we have some model. At the moment
we have choice between 0 and DFc. 0 is not the best estimate as Ed rightly points out. We replace (I am sorry
for self promotion, nevertheless: Murshudov et al, 1997) "absent" reflection with DFc, but it
introduces bias. Bias becomes stronger as the number of "absent" reflections become larger. We need
better way of estimating "unobserved" reflections. In statistics there are few appraoches. None of
them is full proof, all of them are computationally expensive. One of the techniques is called multiple
imputation. It may give better refinement behaviour and less biased map. Another one is integration over all
errors (too many parameters for numerical integration, and there is no closed form formula) of model as well
as experimental data. This would give less bia
sed map with more pronounced signal.
Regards
Garib
On 11 Oct 2011, at 20:15, Randy Read wrote:
If the model is really bad and sigmaA is estimated properly, then sigmaA will
be close to zero so that D (sigmaA times a scale factor) will be close to zero.
So in the limit of a completely useless model, the two methods of map
calculation converge.
Regards,
Randy Read
On 11 Oct 2011, at 19:47, Ed Pozharski wrote:
On Tue, 2011-10-11 at 10:47 -0700, Pavel Afonine wrote:
better, but not always. What about say 80% or so complete dataset?
Filling in 20% of Fcalc (or DFcalc or bin-averaged<Fobs> or else - it
doesn't matter, since the phase will dominate anyway) will highly bias
the map towards the model.
DFc, if properly calculated, is the maximum likelihood estimate of the
observed amplitude. I'd say that 0 is by far the worst possible
estimate, as Fobs are really never exactly zero. Not sure what the
situation would be when it's better to use Fo=0, perhaps if the model is
grossly incorrect? But in that case the completeness may be the least
of my worries.
Indeed, phases drive most of the model bias, not amplitudes. If model
is good and phases are good then the DFc will be a much better estimate
than zero. If model is bad and phases are bad then filling in missing
reflections will not increase bias too much. But replacing them with
zeros will introduce extra noise. In particular, the ice rings may mess
things up and cause ripples.
On a practical side, one can always compare the maps with and without
missing reflections.
--
After much deep and profound brain things inside my head,
I have decided to thank you for bringing peace to our home.
Julian, King of Lemurs
------
Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research Tel: + 44 1223 336500
Wellcome Trust/MRC Building Fax: + 44 1223 336827
Hills Road E-mail: rj...@cam.ac.uk
Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk
Garib N Murshudov
Structural Studies Division
MRC Laboratory of Molecular Biology
Hills Road
Cambridge
CB2 0QH UK
Email: ga...@mrc-lmb.cam.ac.uk
Web http://www.mrc-lmb.cam.ac.uk
