Re: NOE errors -- August 18, 2007 - 11:58

Hi,

This is exactly correct.  The formula you report Seb should be

           sd(NOE) = NOE * sqrt({sd(sat)/I(sat)}^2 + {sd(unsat)/(unsat)}^2).

Note the division rather than the multiplication.  This formula is
directly from Farrow et al. (Biochem. (1994), 33, 5984-6003).  If you
replace the NOE term with the intensity ratio, then take that into the
square root and simplify, you will end up with the formula found
within relax.  The two equivalent equations are both widely reported
in the literature.

Cheers,

Edward


On 8/17/07, Dr Horst Schirra <h.schirra@xxxxxxxxx> wrote:
> 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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