Best way would be to generate from probability distributions derived after refinement, but it has a problem that you need to integrate over all errors. Another, simpler way would be generate using Wilson distribution multiple times and do refinement multiple times and average results. I have not done any tests but on paper it looks like a sensible procedure.
regards Garib On 11 Oct 2011, at 20:58, 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? > > 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 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
