Re: Relax_fit.py problem -- October 14, 2008 - 21:50

Hi,

That was the reference I used many years ago when I first added these
abilities to relax.  The text is a little confusing, but the important
line is the first of that paragraph you mention:

The uncertainties in the measured peak heights, sigma_h, were set
equal to the root-mean-square baseline noise in the spectra.

So if one looks at the code in relax, there is no multiplication by
sqrt(2).  As this was a long time ago, I'm not sure if this is the
most correct approach.  The confusing chi-squared tests between the
sigma_h and sqrt(2)*sigma_h may not statistically significant but
considering that the parameter number is identical in both cases, the
weighting constant simply changes, then no statistically significant
difference doesn't mean that one weight is better than the other or
that both weights are correct.

There is another early reference (or two) in which the NOE error
formula is given.  I think that may have more information, but I'm
struggling to remember what that reference is and cannot find it at
the moment.  And there may be more recent papers performing a much
more thorough noise analysis.  It could even be done using synthetic
spectra with white noise added (I recently did this to test the effect
of white noise on the uncertainty in peak chemical shift position to
validate Ad Bax's RDC error formula LW/SN - strangely the results were
far more complex than this formula).

There is a bit of time to find the correct baseplane RMSD to peak
height uncertainty as I need to wait for Sebastien to finish the work
with the loading of NMRView (as well as Sparky and XEasy) peak list
intensities.  The rearrangements I plan to do will affect the code he
is working on.

Regards,

Edward



On Mon, Oct 13, 2008 at 7:44 PM, Tyler Reddy <TREDDY@xxxxxx> wrote:
> Hi Edward,
>
> Palmer et al. (1991) JACS. 113: 4371-4380 is a nice reference for the error
> conversion. It looks like the value for standard deviation between peaks in
> paired spectra is sqrt(2) multiplied by the base plane RMS value (in
> particular, see the short paragraph at the top right of page 4375 in this
> manuscript). However, the authors seem to use the base plane RMS values
> regardless, and then verify that the qualitative conclusions do not change
> when
> using the more conservative error estimates (i.e. multiplying by 1.4).
>
> There's an extensive discussion of using chi-square critical values to
> verify
> the validity of this relationship between the noise types, though I must
> concede that I don't grasp all the details after the first reading.
>
> Tyler
>
>
> Quoting Edward d'Auvergne <edward.dauvergne@xxxxxxxxx>:
>
> > Hi,
> >
> > There are three ways that an error analysis can be done for relaxation
> > curve fitting, although one of those is only partly implemented in
> > relax at the moment (that means it won't work until I write some
> > computer code).  These are:
> >
> > 1.  Collect all spectra in duplicate, triplicate, or more if you
> > really have lot of NMR time to kill, for absolutely no reason.  The
> > peak intensity error for a single spin is calculated as the standard
> > deviation for each peak.  Because this is inaccurate for a low replica
> > number, this error is averaged for all peaks to give one error per
> > spectrum.  This error is then used in the Monte Carlo simulations.
> >
> > 2.  If only some spectra are duplicated, then the average of the
> > errors for all spectra is calculated.  This gives a single error value
> > for all spins and all spectra.  This is then used in the Monte Carlo
> > simulations.
> >
> > 3.  This is the error analysis technique which is not fully
> > implemented yet.  If no spectra are recorded in duplicate, then one
> > needs to use the RMSD of the base plane noise.  This is similar to
> > what relax uses for the NOE analysis (hence shouldn't be too hard to
> > implement for relaxation curve fitting).  I would need to find the
> > reference, but I think this value needs to be divided or multiplied by
> > root 2 to convert it to a peak height uncertainty.  Does anyone know a
> > reference for this?  Then a separate error value for all spins and all
> > spectra can be used in the Monte Carlo simulations.
> >
> > Wei Xia has recently asked the same question
> > (https://mail.gna.org/public/relax-users/2008-09/msg00000.html).  It
> > might be worth reading my reply at
> > https://mail.gna.org/public/relax-users/2008-09/msg00002.html.  So
> > this feature will be added to relax, but the question is how long will
> > that take.  I'd first need the error conversion factor from RMSD of
> > base plane noise to peak height, and then add the ability to use the
> > RMSD value in relaxation curve fitting.  The first part will be the
> > hardest, but you'll need that to do a proper Monte Carlo simulation
> > error analysis for the curve fitting.  To do the second part I would
> > set up a mini analysis, lets call it a 'system test' because it tests
> > the system - relax - to see if the analysis works, and then make this
> > system test pass - i.e. implement the feature.
> >
> > Don't forget that the errors in a complex analysis (e.g model-free and
> > reduced spectral density mapping) are just as important as the values
> > themselves, if not more.  Getting these wrong will really damage
> > optimisation, model selection, and error propagation to the final
> > parameters via Monte Carlo simulations.  So both your model-free
> > values and errors will be incorrect.
> >
> > Regards,
> >
> > Edward
> >
> >
> > On Wed, Oct 8, 2008 at 5:07 PM, Tyler Reddy <TREDDY@xxxxxx> wrote:
> > > Hello,
> > >
> > > It seems that Relax_fit.py requires replicate data because average and
> > > standard
> > > deviation values are used downstream in the analysis. With no replicate
> > > data
> > > (since I don't have any) the output is shown below. Also, commenting out
> > > the
> > > average and error propagation across multiple spectra
> > >
> > > #relax_fit.mean_and_error()
> > >
> > > doesn't work either, and I get another error output that is looking for
> > > an
> > > averaged value. I'll probably try using a duplicate data set to
> > > circumvent this
> > > for now (unless this is actually another problem).
> > >
> > > Tyler
> > >
> > > Output:
> > >
> > > relax> relax_fit.mean_and_error()
> > >
> > > Calculating the average intensity and standard deviation of all spectra.
> > >
> > > Time point:  0.01 s
> > > Number of spectra:  1
> > > Standard deviation for time point 0:  0.0
> > >
> > > Time point:  0.050000000000000003 s
> > > Number of spectra:  1
> > > Standard deviation for time point 1:  0.0
> > >
> > > Time point:  0.10000000000000001 s
> > > Number of spectra:  1
> > > Standard deviation for time point 2:  0.0
> > >
> > > Time point:  0.20000000000000001 s
> > > Number of spectra:  1
> > > Standard deviation for time point 3:  0.0
> > >
> > > Time point:  0.29999999999999999 s
> > > Number of spectra:  1
> > > Standard deviation for time point 4:  0.0
> > >
> > > Time point:  0.5 s
> > > Number of spectra:  1
> > > Standard deviation for time point 5:  0.0
> > >
> > > Time point:  0.80000000000000004 s
> > > Number of spectra:  1
> > > Standard deviation for time point 6:  0.0
> > > Traceback (most recent call last):
> > >  File "/Applications/relax-1.3.1/relax", line 408, in <module>
> > >   Relax()
> > >  File "/Applications/relax-1.3.1/relax", line 125, in __init__
> > >   self.interpreter.run(self.script_file)
> > >  File "/Applications/relax-1.3.1/prompt/interpreter.py", line 270, in run
> > >   return run_script(intro=self.__intro_string, local=self.local,
> > > script_file=script_file, quit=self.__quit_flag,
> > > show_script=self.__show_script,
> > > raise_relax_error=self.__raise_relax_error)
> > >  File "/Applications/relax-1.3.1/prompt/interpreter.py", line 531, in
> > > run_script
> > >   return console.interact(intro, local, script_file, quit,
> > > show_script=show_script, raise_relax_error=raise_relax_error)
> > >  File "/Applications/relax-1.3.1/prompt/interpreter.py", line 427, in
> > > interact_script
> > >   execfile(script_file, local)
> > >  File "relax_fit_T1_500Mhz.py", line 45, in <module>
> > >   relax_fit.mean_and_error()
> > >  File "/Applications/relax-1.3.1/prompt/relax_fit.py", line 96, in
> > > mean_and_error
> > >   relax_fit_obj.mean_and_error()
> > >  File "/Applications/relax-1.3.1/specific_fns/relax_fit.py", line 729, in
> > > mean_and_error
> > >   sd = sd / float(num_dups)
> > > ZeroDivisionError: float division
> > >
> > >
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