Hi Edward. With my scribbles, and notes from my statistics book, I derive almost the same thing.
My problem is that I end up with also wanting the time for the reference point. And that does not make sense. It reminds me of the NS R1rho equation problem, with 1/T. Best Troels Troels Emtekær Linnet 2014-09-01 15:08 GMT+02:00 Edward d'Auvergne <[email protected]>: > Ok, I've found one reference for this formula: > > - Loria, J. P. and Kempf, J. G. (2004) Measurement of > Intermediate Exchange Phenomena. Methods in Molecular Biology, 278, > 185-231. (http://dx.doi.org/10.1385/1-59259-809-9:185). > > Specifically section 3.2.7.1 "Two-Point Data Sampling", and equation 22: > > R2(tau_CP^-1) = t^-1 ln[ave(I0) / ave(I(t))] +/- t^-1 Delta_Q, > > and equation 23: > > Delta_Q = sqrt(Delta_I0^2 + Delta_I(t)^2). > > This is apparently from the book: > > - Shoemaker, D. P., Garland, C. W., and Nibler, J. W. (1989) > Experiments in Physical Chemistry. 5th ed. McGraw-Hill, New York. > > Though I don't have access to that to check. > > Regards, > > Edward > > > > On 1 September 2014 10:55, Edward d'Auvergne <[email protected]> wrote: >> 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 <[email protected]> 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 <[email protected]>: >>>> 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 <[email protected]> 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" <[email protected]> >>>>> 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 <[email protected]>: >>>>>> > 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 <[email protected]>: >>>>>> >> 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 <[email protected]> >>>>>> >> 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 <[email protected]>: >>>>>> >>>> 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 >>>>>> >>>> <[email protected]> wrote: >>>>>> >>>>> Do you mean terrible or double? >>>>>> >>>>> >>>>>> >>>>> Best >>>>>> >>>>> Troels >>>>>> >>>>> >>>>>> >>>>> 2014-08-29 16:15 GMT+02:00 Edward d'Auvergne >>>>>> >>>>> <[email protected]>: >>>>>> >>>>>> 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 >>>>>> >>>>>> [email protected] >>>>>> >>>>>> >>>>>> >>>>>> 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 [email protected] 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
