Hi Ed,
Thanks for all the info, its very useful. So I have two questions now.
What is the evidence, if any, that the exptl sigmas are actually negligible compared to fit beta (is it alluded to in Lunin 2002)? Is there somewhere in phenix output I can verify this myself?
And, in comparison, how does refmac handle the exptl sigmas? Maybe this last question is more appropriate for ccp4bb, but contrasting with phenix would be helpful for me. I know there's a box, checked by default, "Use exptl sigmas to weight Xray terms".
Cheers,
D
On Dec 10, 2012, at 1:04 PM, Ed Pozharski <epozh001(a)UMARYLAND.EDU> wrote:
> On 12/06/2012 05:35 PM, Douglas Theobald wrote:
>
>> However, I was surprised to hear rumors that with phenix "the data are not properly weighted in refinement by incorporating observed sigmas" and such.
> Douglas,
>
> Up to a certain point in its derivation, maximum likelihood target is
> exactly the same in all implementations. Where Lunin/cctbx/phenix
> approach is different is that it derives analytical expressions for
> model error parameters by optimization of the maximum likelihood target
> itself with respect to these. It's a clever approach, except that it
> does not work unless one ignores experimental errors.
>
> A minimization target contains essentially a difference between
> calculated and observed structural amplitudes (properly scaled etc).
> For each reflection it must be properly weighted by combined
> uncertainty, which includes both model error and experimental error.
> Assume that former is much larger than the latter which can then be
> ignored. Both errors are now combined in a single parameter (per
> resolution shell, called beta), which can be calculated analytically.
> Once this is done, we go back and check - and indeed, this combined
> model error is larger than the experimental one.
>
> There are few interesting consequences of this.
>
> First, it seems clear that weighting every reflection in a resolution
> shell the same way is a compromise. One expects less precisely measured
> reflections should be weighted down. But the effect may be small.
>
> Second, mathematically it turns out that the target value (towards which
> Fc is pushed) for some reflections should be set to exactly zero. The
> cutoff is Fo<sqrt(es*beta). Quote from Lunin et al., 2002:
>
> "...in this case, the likelihood-based target fits the calculated
> magnitude to the zero value (Fs*=0) regardless of the particular value
> of Fobs."
>
> Third, one is tempted to interpret the beta parameter as the model
> variance. The problem is sqrt(beta) ends up significantly higher than
> one would expect from the R-values. This, imho, poses a bit of a problem
> in light of the second issue - resetting Fs* to zero for "weak
> reflections". If beta ends up overestimated for whatever reason, then
> those reflections aren't that weak anymore.
>
> Yet, the refinement still seems to work just fine. So perhaps
> overestimated model error is not a big deal in that respect. Indeed it
> is not. In fact, one can multiply beta by arbitrary number, and the
> relative weight applied to individual reflections in maximum likelihood
> will remain roughly the same. So while it provides robust
> resolution-dependent weighting, the absolute value of beta parameter is
> not easily interpreted (as absolute model error).
>
> Hopefully all is well in sunny Waltham,
>
> Ed.
>
> --
> Oh, suddenly throwing a giraffe into a volcano to make water is crazy?
> Julian, King of Lemurs
>
>
