Hi Sebastien,
Nope - Error propagation works according to Gauss like:
[sigma(f(a,b,...))]^2= [df/da]^2 * [sigma(a)]^2 + [df/db]^2 *
[sigma(b)]^2 + ....
In other words the variance (square of the standard deviation) of a
function f that depends on variables a,b,... is the sqare of the partial
derivative of f with respect to a [1], times the square of the standard
deviation of a [2] + the square of the partial derivative of f with
respect to b times the square of the standard deviation of b + and so on...
For NOE=a/b you get:
dNOE/da = 1/b
dNOE/db = -a/(b^2)
If you insert that into the formula above and take the square root at
the end to get sigma(NOE) instead of sigma(NOE)^2 then you end up with
Ed's formula.
Cheers,
Horst Joachim Schirra
[1]=(possibly better written in the proper form as [d f(a,b,...)/da]^2 -
but I wanted to save space up there)
[2]= In other words: the variance of a
----------------------------------------------------------------
/ Dr. sc. nat. Horst Joachim Schirra Phone: (+61)7/3346-2021 /
/ Queensland Smart State Fellow Fax: (+61)7/3346-2101 /
/ Institute for Molecular Bioscience /
/ University of Queensland email: h.schirra@xxxxxxxxx /
/ Brisbane QLD 4072, Australia http://www.uq.edu.au/~uqhschir /
----------------------------------------------------------------
----- Original Message -----
From: Sebastien Morin <sebastien.morin.1@xxxxxxxxx>
Date: Friday, August 17, 2007 3:37 am
Subject: NOE errors
Hi everyone,
I was looking at the NOE tool in relax and was quite surprised by the
way errors are calculated...
In the file 'specific_fns/noe.py' of the 1.2 line (r3354), the
functionfor the noe error is :
_____________________________________________
\/ {sd(sat)*I(unsat)}^2 + {sd(unsat)*I(sat)}^2
sd(NOE) = ----------------------------------------------
-
I(unsat)^2
Shouldn't this be more like :
_____________________________________________ sd(NOE) =
NOE * \/ {sd(sat)*I(sat)}^2 + {sd(unsat)*I(unsat)}^2
In other words, shouldn't the NOE error be the product of the NOE
by the
root of the squared sum of relative errors for Isat and Iunsat,
respectively ? Ain't this the way one should normally propagate errors
for value calculated by a division (like NOE=Isat/Iunsat)
What are the main advantages of calculating errors with either
techniques and why the one is relax should be more accurate ?
Thanks !
Sébastien
--
______________________________________
_______________________________________________
| |
|| Sebastien Morin ||
||| Etudiant au PhD en biochimie |||
|||| Laboratoire de resonance magnetique nucleaire ||||
||||| Dr Stephane Gagne |||||
|||| CREFSIP (Universite Laval, Quebec, CANADA) ||||
||| 1-418-656-2131 #4530 |||
|| ||
|_______________________________________________|
______________________________________
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Re: NOE errors