Hi Troels, The 2-point exponential error formula is currently equation 11.4 in the relax manual (http://www.nmr-relax.com/manual/R2eff_model.html). I unfortunately did not write down a reference for it. But the equation is in a number of dispersion papers - I just have to find it. Feel free to search yourself. I also simulated this error, see figure 11.1 in the relax manual (http://www.nmr-relax.com/manual/R2eff_model.html#fig:_dispersion_error_comparison)
Regards, Edward On 30 August 2014 13:49, Troels Emtekær Linnet <tlin...@gmail.com> wrote: > Hi Edward. > > I found this old post in gwing gwong doogle Google. > http://thread.gmane.org/gmane.science.nmr.relax.scm/17553 > > And then I see, that for a two point exponential, this i just > converting the values to a linear problem. > > For several time points, a good initial guess for estimating r2eff, > and i0, by converting to a linear problem, and solving by linear least > squares. > (This is currently the experimental 'estimate_x0_exp' in the R2eff > estimate module). > Maybe I should try some weighting on this. > > --------- > # Convert to linear problem. > # Func > # I = i0 exp(-t R) > # Convert to linear > # ln(I) = R (-t) + ln(i0) > # Compare > # f(I) = a x + b > > ln_I = log(I) > x = - 1. * times > n = len(times) > > # Solve by linear least squares. > a = (sum(x*ln_I) - 1./n * sum(x) * sum(ln_I) ) / ( sum(x**2) - 1./n * > (sum(x))**2 ) > b = 1./n * sum(ln_I) - b * 1./n * sum(x) > > # Convert back from linear to exp function. Best estimate for parameter. > r2eff_est = a > i0_est = exp(b) > ----------- > > And then I see in And then I look in lib.dispersion.two_point.py > > --------------- > """Calculate the R2eff/R1rho error for the fixed relaxation time data. > > The formula is:: > > __________________________________ > 1 / / sigma_I1 \ 2 / sigma_I0 \ 2 > sigma_R2 = ------- / | -------- | + | -------- | > relax_T \/ \ I1(nu1) / \ I0 / > > where relax_T is the fixed delay time, I0 and sigma_I0 are the > reference peak intensity and error when relax_T is zero, and I1 and > sigma_I1 are the peak intensity and error in the spectrum of interest. > ------------- > > Right now, I don't know where that comes from. > > My reference book: > An introduction to Error Analysis, Second Edition > John R. Taylor > http://www.uscibooks.com/taylornb.htm > > "You will not be surprised to learn that when the uncertainties ... > are independent and random, the sum can be replaced by a sum in > quadrature." > > So, just following you analogy, I could get sigma R2 this way. > > I will look into it and make some tests scripts. > > > > > Troels Emtekær Linnet > > > 2014-08-30 9:54 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >> Hi, >> >> I don't have much time to reply now, but the key is it use simple >> synthetic noise-free data. Try converting the 5 intensities in >> test_suite/shared_data/curve_fitting/numeric_topology/ into 5 Sparky >> peak lists with a single spin. Then test the Monte Carlo simulations >> and covariance matrix user functions in relax. These two relax >> techniques should then match the numeric results from the super-basic >> scripts in that directory! This would then be converted into two >> system tests. >> >> This was my plan, to complete in my spare time. If you want to go >> quickly, then feel free to follow these steps yourself rather than >> waiting for me to do it. I actually suggested this synthetic data >> testing earlier to you >> (http://thread.gmane.org/gmane.science.nmr.relax.devel/6807/focus=6840). >> Synthetic noise-free data is an essential tool for implemented and >> debugging any new analysis type, algorithm, protocol, etc. The key is >> that you know the answer you are searching for! And synthetic data is >> simple. Nothing should ever be implemented and debugged using real >> data, as a good looking result might be the consequence of a nasty >> bug. >> >> Regards, >> >> Edward >> >> >> >> >> >> >> On 30 August 2014 02:49, Troels Emtekær Linnet <tlin...@gmail.com> wrote: >>> Hm. >>> >>> The last idea I have, is the division by number of degree of freedom. >>> >>> So either 5-2, or 4-2. >>> >>> That should be verified by a script with many different time points. >>> >>> But then the errors for intensity gets very different. >>> >>> Hm. >>> >>> On 30 Aug 2014 01:45, "Troels Emtekær Linnet" <tlin...@nmr-relax.com> wrote: >>>> >>>> The sentence: >>>> >>>> "then the covariance matrix above gives the statistical error on the >>>> best-fit parameters resulting from the Gaussian errors 'sigma_i' on >>>> the underlying data 'y_i'." >>>> >>>> And here I note the wording: >>>> "statistical error" >>>> "Gaussian errors" >>>> >>>> Best >>>> Troels >>>> >>>> >>>> 2014-08-29 21:21 GMT+02:00 Troels Emtekær Linnet <tlin...@nmr-relax.com>: >>>> > Hi Edward. >>>> > >>>> > I also think it is some math some where. >>>> > >>>> > I have a feeling, that it is the creating of Monte Carlo data with 2 >>>> > sigma? >>>> > and then some log/exp calculation of R2eff. >>>> > >>>> > If the errors are 2 x times over estimated, the chi2 values are 4 as >>>> > small, and the >>>> > space should be the same? >>>> > >>>> > best >>>> > Troels >>>> > >>>> > 2014-08-29 17:06 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>> >> I've just added the 2D Grace plots for this to the repository (r25444, >>>> >> http://article.gmane.org/gmane.science.nmr.relax.scm/23194). They are >>>> >> also attached to the task for easier access >>>> >> (https://gna.org/task/index.php?7822#comment107). From these plots I >>>> >> see that the I0 error appears to be reasonable, but that the R2eff >>>> >> errors are overestimated by 1.9555. >>>> >> >>>> >> The plots are very, very different. It is clear that >>>> >> chi2_jacobian=True just gives rubbish. It is also clear that there is >>>> >> a perfect correlation in R2eff when chi2_jacobian=False. The plot >>>> >> shows absolutely no scattering, therefore this indicates a crystal >>>> >> clear mathematical error somewhere. I wonder where that could be. It >>>> >> may not be a factor of 2, as the correlation is 1.9555. So it might >>>> >> be a bug that is more complicated. In any case, overestimating the >>>> >> errors by ~2 and performing a dispersion analysis is not possible. >>>> >> This will significantly change the curvature of the optimisation space >>>> >> and will also have a huge effect on statistical comparisons between >>>> >> models. >>>> >> >>>> >> Regards, >>>> >> >>>> >> Edward >>>> >> >>>> >> >>>> >> >>>> >> On 29 August 2014 16:56, Troels Emtekær Linnet <tlin...@nmr-relax.com> >>>> >> wrote: >>>> >>> The default is now chi2_jacobian=False. >>>> >>> >>>> >>> You will hopefully see, that the errors are double. >>>> >>> >>>> >>> Best >>>> >>> Troels >>>> >>> >>>> >>> 2014-08-29 16:43 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>> >>>> Terrible ;) For R2eff, the correlation is 2.748 and the points are >>>> >>>> spread out all over the place. For I0, the correlation is 3.5 and >>>> >>>> the >>>> >>>> points are also spread out everywhere. Maybe I should try with the >>>> >>>> change from: >>>> >>>> >>>> >>>> relax_disp.r2eff_err_estimate(chi2_jacobian=True) >>>> >>>> >>>> >>>> to: >>>> >>>> >>>> >>>> relax_disp.r2eff_err_estimate(chi2_jacobian=False) >>>> >>>> >>>> >>>> How should this be used? >>>> >>>> >>>> >>>> Cheers, >>>> >>>> >>>> >>>> Edward >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> On 29 August 2014 16:33, Troels Emtekær Linnet >>>> >>>> <tlin...@nmr-relax.com> wrote: >>>> >>>>> Do you mean terrible or double? >>>> >>>>> >>>> >>>>> Best >>>> >>>>> Troels >>>> >>>>> >>>> >>>>> 2014-08-29 16:15 GMT+02:00 Edward d'Auvergne <edw...@nmr-relax.com>: >>>> >>>>>> Hi Troels, >>>> >>>>>> >>>> >>>>>> I really cannot follow and judge how the techniques compare. I >>>> >>>>>> must >>>> >>>>>> be getting old. So to remedy this, I have created the >>>> >>>>>> >>>> >>>>>> test_suite/shared_data/dispersion/Kjaergaard_et_al_2013/exp_error_analysis/ >>>> >>>>>> directory (r25437, >>>> >>>>>> http://article.gmane.org/gmane.science.nmr.relax.scm/23187). This >>>> >>>>>> contains 3 scripts for comparing R2eff and I0 parameters for the 2 >>>> >>>>>> parameter exponential curve-fitting: >>>> >>>>>> >>>> >>>>>> 1) A simple script to perform Monte Carlo simulation error >>>> >>>>>> analysis. >>>> >>>>>> This is run with 10,000 simulations to act as the gold standard. >>>> >>>>>> >>>> >>>>>> 2) A simple script to perform covariance matrix error analysis. >>>> >>>>>> >>>> >>>>>> 3) A simple script to generate 2D Grace plots to visualise the >>>> >>>>>> differences. Now I can see how good the covariance matrix >>>> >>>>>> technique >>>> >>>>>> is :) >>>> >>>>>> >>>> >>>>>> Could you please check and see if I have used the >>>> >>>>>> relax_disp.r2eff_err_estimate user function correctly? The Grace >>>> >>>>>> plots show that the error estimates are currently terrible. >>>> >>>>>> >>>> >>>>>> Cheers, >>>> >>>>>> >>>> >>>>>> Edward >>>> >>>>>> >>>> >>>>>> _______________________________________________ >>>> >>>>>> relax (http://www.nmr-relax.com) >>>> >>>>>> >>>> >>>>>> This is the relax-devel mailing list >>>> >>>>>> relax-devel@gna.org >>>> >>>>>> >>>> >>>>>> To unsubscribe from this list, get a password >>>> >>>>>> reminder, or change your subscription options, >>>> >>>>>> visit the list information page at >>>> >>>>>> https://mail.gna.org/listinfo/relax-devel _______________________________________________ relax (http://www.nmr-relax.com) This is the relax-devel mailing list relax-devel@gna.org To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel
