[phenixbb] Cross Validation Reflection Set question

Dale Tronrud det102 at uoxray.uoregon.edu
Mon Nov 7 09:52:07 PST 2011

   This answer confuses two independent properties of a refinement - the target
function and the optimization method.  Rigid body refinement is required because
the target function (whatever it is) is being optimized with a method that assumes
that off-diagonal elements of the second derivative matrix are small.  When
correction of the errors in the model requires the concerted motion of groups of
atoms the off-diagonal elements of this matrix are very large and the assumption
that they are not causes the error to be uncorrected.  Forcing rigid body
refinement reparameterizes the model so that the new second derivative matrix
really has small off-diagonal elements and the optimization can correct the problem.

   Low resolution data are sufficient to define the optimal rigid body parameters.
With the least-squares target the presence of the high resolution data reduced
the radius of convergence of the optimization making the reduction of the resolution
limit mandatory.  A good ML target should set all the high resolution gradients
to zero making them irrelevant.  As has been mentioned elsewhere, since it is just
a very computationally expensive way to calculate zero one can save time by reducing
the resolution limit anyway.

   I should emphasize "good" in good ML target.  The calculation of sigma A, itself,
assumes that the atomic positional errors are uncorrelated, so the currently used
ML target is not a "good" ML target for models with this type of error.  This is what,
I believe, is the cause of the resolution limit effects reported in Afonine's 2009

Dale Tronrud

On 11/06/11 18:59, Pavel Afonine wrote:
> Hi,
>> Open question,
>> Is this 'step wise resolution increase' still necessary in the days of
>> maximum likelihood refinement?
> it not really open question. If ML target was that powerful you could do
> rigid body refinement using all reflections without the need of cutting
> off high resolution. It's not the case however, as we show in
> Automatic multiple-zone rigid-body refinement with a large convergence
> radius. P. V. Afonine, R. W. Grosse-Kunstleve, A. Urzhumtsev and P. D.
> Adams J. Appl. Cryst. 42, 607-615 (2009).
> STIR may be necessary for example in case of "very poor" starting model
> and "very high" resolution data, although the whole procedure should
> probably be more complex: for example, model parametrization should
> change as more higher resolution data is added.
> Pavel
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