> -----Original Message-----
> From: [log in to unmask] 
> [mailto:[log in to unmask]] On Behalf Of Jon Wright
> Sent: 08 September 2008 21:29
> To: Borhani, David
> Cc: [log in to unmask]
> Subject: Re: [ccp4bb] truncate ignorance
> 
> Borhani, David wrote:
> > ...
> >  but I think pretty much everyone has converged on using it for the
> > past many years.
> 
> Many small molecule crystallographers seem to refine on 
> intensity and so 
> avoid need this procedure. Towards the end of the recent 
> thread "Wilson 
> plot from truncated.mtz" it had seemed like this forum was 
> starting to 
> see that light?
> 
> In short - if your observations are supposed to be noisy in the 
> "plus_or_minus sigma" sense then the peaks which are much 
> less than the 
> sigma should come out negative almost half of the time. 
> Truncate would 
> appear to be for the case where you want an estimate of the true 
> magnitude of the structure factor, "F", and not your 
> experimental data.
> 
> Jon
> 
> 

This can't be correct, for whatever you say is true for F must also hold
equally for I, in other words if you accept that the Truncate procedure
is valid for getting a better estimate of the true F (and I think we're
all agreed that it is valid), then logically it must also be valid for
getting a better estimate of the true I.  The point is that F, as the
sqrt of a +ve I, is needed for computing an electron density map,
whereas you don't need an improved estimate for I to do I-based
refinement, since the measured I serves equally well.

Note however that since the corrected I's really are better estimates,
you will get lower I-based R factors (both Rwork & Rfree) from an
I-based refinement (note well that the corrected I is NOT the same as
the [corrected F]^2, i.e. you must NOT square the F's to do an I-based
refinement, you must go back to the original I's).  However as we all
know (or should know by now!), getting better R factors doesn't
necessarily imply that you will get a better structure, and since you
have not added any more information in the Truncate procedure over and
above that which you are already inputting into the refinement (namely
the unit cell contents), it's very hard to see how you could get a
better structure.

Note also that George Sheldrick suggested in an earlier thread that the
corrected I's are biased, referring to the situation where the average
true I is zero, but thinking about this further I'm sure this is not
correct.  The reason is that if the average true I is zero, the Wilson
distribution is a Dirac delta function (infinite spike) at I=0; this
overrides any distribution of the measured I in the Bayes equation, so
the corrected I's, and hence the average corrected I, are also exactly
zero, hence there is no bias.  In the general case, whilst it is true
that the negative I's are increased when the correction is performed,
many (not all) positive I's are decreased (because they are all shifted
towards the peak of the Wilson probability density at I=0), so the net
effect is that the average I is unchanged.

I believe also that in an earlier posting Peter Zwart said he thought
that CNS doesn't take account of the Wilson distribution when doing its
version of the correction; if this is true (and I have no independent
evidence that it is since I'm not a CNS user), then the above argument
implies that the F's corrected by such a procedure will inevitably be
biased, though the damage done may well not be significant compared with
that done by using F's instead of I's in the first place.

-- Ian


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