Fulvio, Tim,
error propagation is correct, but wrongly applied in Tim's example.
s_f= \sqrt{ \left(\frac{\partial f}{\partial {x} }\right)^2 s_x^2 +
\left(\frac{\partial f}{\partial {y} }\right)^2 s_y^2 +
\left(\frac{\partial f}{\partial {z} }\right)^2 s_z^2 + ...} (see
http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification)
The uncertainty in a derived magnitude is always larger than any
individual uncertainty, so no subtraction, anytime. Furthermore, in
Tim's example you could end up with negative sigmas..
HTH,
Jens
On Thu, 2013-11-07 at 04:44 +0100, Tim Gruene wrote:
> Dear Fulvio,
>
> with simple error propagation, the error would be
> sigma(I(h1)) = (1-α)sigma(Iobs(h1))-α*sigma(Iobs(h2))/(1-2α)
>
> would it not?
>
> Although especially for theoretical aspects you should be concerned
> about division by zero.
>
> Best,
> Tim
>
> On 11/06/2013 05:54 PM, Fulvio Saccoccia wrote:
> > Thank you for reply. My question mostly concern a theoretical
> > aspect rather than practical one. To be not misunderstood, what is
> > the mathematical model that one should apply to be able to deal
> > with twinned intensities with their errors? I mean, I+_what? I ask
> > this In order to state some general consideration on the accuracy
> > about the recovery the true intensities on varying of alpha. Thanks
> > Fulvio
> >
> > Fulvio Saccoccia PhD Dept. of Biochemical Sciences Sapienza
> > University of Rome 5, Piazzale A. Moro 00185 phone +39 0649910556
> >
> > ----Messaggio Originale---- Da: herman.schreu...@sanofi.com
> > Inviato: 06/11/2013, 17:25 A: CCP4BB@JISCMAIL.AC.UK Oggetto:
> > [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities
> > from twinned crystals
> >
> >
> > Dear Fulvio, you cannot detwin perfectly twinned data with this
> > formula. The term (1-2α) becomes zero, so you are dividing by zero.
> > With good refinement programs (ShelX, Refmac), refinement is done
> > against twinned data, which is better than to detwin the data with
> > the formula you mention.
> >
> > As I understand it, to get map coefficients, the calculated
> > contribution of the twin domain (Fcalc’s) is substracted from Fobs
> > (with the appropriate weighting factors), so what you see in coot
> > is detwinned electron density. In practical terms, the only thing
> > you have to do is to specify the TWIN keyword in Refmac.
> >
> > Best regards, Herman
> >
> >
> >
> > Von: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] Im Auftrag
> > von Fulvio Saccoccia Gesendet: Mittwoch, 6. November 2013 16:58 An:
> > CCP4BB@JISCMAIL.AC.UK Betreff: [ccp4bb] uncertainites associated
> > with intensities from twinned crystals
> >
> >
> > Dear ccp4 users
> >
> > a question about the recovering of true intensities from merohedral
> > twinned crystal. Providing alpha and the twin operator one should
> > be able to recover the intensities from the formulas:
> >
> >
> >
> > I(h1) = (1-α)Iobs(h1)-αIobs(h2)/(1-2α)
> >
> > I(h2) = -αIobs(h1)+(1+α)Iobs(h2)/(1-2α)
> >
> > as stated in many papers and books*.
> >
> > However I was wondering about the uncertainties associated to these
> > measurements, I mean: for all physical observable an uncertainty
> > should be given.
> >
> > Hence, what is the uncertainty associated to a perfect merohedrally
> > twinned crystal (alpha=0.5)? It is clear that in this case we drop
> > in a singular value of the above formulas.
> >
> > Please, let me know your hints or your concerns on the matter.
> > Probably there is something that it is not so clear to me.
> >
> >
> >
> > Thanks in advance
> >
> >
> >
> > Fulvio
> >
> >
> >
> >
> >
> > ref. **(C. Giacovazzo, H. L. Monaco, G. Artioli, D. Viterbo, M.
> > Milaneso, G. Ferraris, G. Gilli, P. Gilli, G. Zanotti and M. Catti.
> > Fundamentals of Crystallography, 3rd edition. IUCr Texts on
> > Crystallography No. 15, IUCr/Oxford University Press, 2011;
> > Chandra, N., Acharya, K. R., Moody, P. C. (1999). Acta Cryst. D55.
> > 1750-1758)
> >
> > --
> >
> > Fulvio Saccoccia, PhD
> >
> > Dept. of Biochemical Sciences "A. Rossi Fanelli"
> >
> > Sapienza University of Rome
> >
> > Tel. +39 0649910556
> >
>
