On Thu, Oct 16, 2008 at 3:11 PM, Sébastien Morin
<sebastien.morin.1@xxxxxxxxx> wrote:
Hi,
I have a general question about curve fitting within relax.
Let's say I proceed to curve fitting for some relaxation rates
(exponential decay) and that I have a duplicate delay for error estimation.
========
delays
0.01
0.01
0.02
0.04
...
========
Will the mean value (for delay 0.01) be used for curve fitting and rate
extraction ?
Or will both values at delay 0.01 be used during curve fitting, hence
giving more weight on delay 0.01 ?
In other words, will the fit only use both values at delay 0.01 for
error estimation or also for rate extraction, giving more weight for
this duplicate point ?
How is this handled in relax ?
Instinctively, I would guess that the man value must be used for
fitting, as we don't want the points that are not in duplicate to count
less in the fitting procedure... Am I right ?
I would argue not. If we have gone to the trouble of measuring
something twice (or, equivalently, measuring it with greater
precision) then we should weight it more strongly to reflect that.
So we should include both duplicate points in our fit, or we should
just use the mean value, but weight it to reflect the greater
certainty we have in its value.
As I type this I realise this is likely the source of the sqrt(2)
factor Tyler and Edward have been debating on a parallel thread - the
uncertainty in height of any one peak is equal to the RMS noise, but
the std error of the mean of duplicates is less by a factor of
sqrt(2).
Chris
Re: Curve fitting