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: [log in to unmask] 
> Inviato:  06/11/2013, 17:25 A: [log in to unmask] 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:[log in to unmask]] Im Auftrag
> von Fulvio Saccoccia Gesendet: Mittwoch, 6. November 2013 16:58 An:
> [log in to unmask] 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
>