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: [email protected]
> > 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: [email protected]
> 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
