Dear Jens, That formula for error propagation is correct for independent measurements. Does this assumption stand true for Intensities in twinning? I am no expert, but I would think not.
Tassos On 7 Nov 2013, at 7:53, Jens Kaiser wrote: > Fulvio, Tim, > error propagation is correct, but wrongly applied in Tim's example. > (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: [email protected] >> > Inviato: 06/11/2013, 17:25 A: [email protected] 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:[email protected]] Im Auftrag >> > von Fulvio Saccoccia Gesendet: Mittwoch, 6. November 2013 16:58 An: >> > [email protected] 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 >> > >> >
