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 biased 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
