On Wednesday, October 12, 2011 01:12:11 pm Edward A. Berry wrote:
> Tim Gruene wrote:
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> >
> >
> > On 10/11/2011 09:58 PM, Ethan Merritt wrote:
> >> 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?
> >
> > Some people call this the "free-lunch-algorithm" ;-)
> > Tim
> >
> Doesn't work- the Fourier transform is invertable. As someone already said in
> this
> thread, if the map was made with coefficients of zero for certain reflections
> (which is equivalent to omitting those reflections) The back-transform will
> give zero for those reflections. Unless you do some density modification
> first.
> So free-lunch is a good name- there aint no such thing!
Tim refers to the procedure described in
Sheldrick, G. M. (2002). Z. Kristallogr. 217, 644–65
which was later incorporated into shelxe as the Free Lunch Algorithm.
It does indeed involve a form of density modification.
Tim is also correct that this procedure is the precedent I had in mind,
although I had forgotten its clever name.
cheers,
Ethan
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
University of Washington, Seattle 98195-7742
