On Tuesday, October 11, 2011 12:33:09 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.
I don't quite follow how one would generate multiple imputations in this case. Would this be equivalent to generating a map from (Nobs - N) refls, then filling in F_estimate for those N refls by back-transforming the map? Sort of like phase extension, except generating new Fs rather than new phases? Ethan > 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. > >> > > > > ------ > > 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 > > > > -- Ethan A Merritt Biomolecular Structure Center, K-428 Health Sciences Bldg University of Washington, Seattle 98195-7742