Hi Troels, I'm still trying to work out what is happening, as R2eff errors being overestimated by 1.9555 is not good enough for any subsequent analysis (http://thread.gmane.org/gmane.science.nmr.relax.devel/6929/focus=6935). It's as bad as doubling your values - the accuracy of the errors and values are of equal importance. I've numerically integrated a simple test system using the numdifftools Python package to obtain the Jacobian (and pseudo-Jacobian of the chi-squared function). And I then created unit tests to check the target_function.relax_fit C module jacobian() and jacobian_chi2() functions. This shows that these functions are 100% bug-free and operate perfectly. I'm now searching for an external tool for numerically approximating the covariance matrix.
To this end, could you maybe shift the specific_analyses.relax_disp.estimate_r2eff.multifit_covar() function into the lib.statistics package? This is a very useful, stand-alone function which is extremely well documented and uses a very robust algorithm. It would be beneficial for future uses including using it in other analysis types. Using this to create an analysis independent error_analysis.covariance_matrix user function is rather trivial and would be of great use for all. By debugging, I can see that multifit_covar() returns exactly the same result as inv(J^T.W.J). So it should be correct. However I really would like to have this basic synthetic data numerical approximation to compare it to via unit testing. As for the error scaling factors of [1.9555, 0.9804] for the parameters [R2eff, I0], that is still a total mystery. Maybe it is better for now to give up on the idea of using the covariance matrix as a quick error estimate :( Regards, Edward On 29 August 2014 13:11, Troels Emtekær Linnet <tlin...@nmr-relax.com> wrote: > Hi Edward. > > I thing the estimation for of r2eff errors via Co-variance matrix > should be considered complete. > > The facts: > > We get the same co-variance as reported by scipy.minimise.leastsq. > > Using the direct exponential Jacobian, seems to give double error on > R2eff, but after fitting, > the extracted parameters of 'r1', 'r2', 'pA', 'dw', 'kex' are very similar. > > The chi2 values seems 4x as small, but that agrees with the R2eff > errors being 2x as big. > > This should complete the analysis. > > I have not found any "true" reference to which Jacobian to use. > I think it is my imagination, to use the chi2 function Jacobian. > > It seems from various tutorials also refers to the direct Jacobian: > http://www.orbitals.com/self/least/least.htm > > This is an experimental feature, and that is pointed out in the user function. > > The last point here is, that it seems that just 50 Monte-Carlo > simulations is enough for the > estimation of R2eff errors. > > After your implementation in C-code of the Jacobian, and the Hessian, > which give the possibility to use "Newton" as minimisation technique, > Monte-Carlo simulations are now so super-fast, that if one is in a > HURRY, at least 50 MC simulations will give a better, and more safe, > result than estimating from the Co-Variance matrix. > > But now the option is there, giving freedom to the user to try > different possibilities. > > I think the code should reside where it is, since it is still so experimental. > When the usability has been verified, it could be split up. > If the usability is low, then one can quickly delete it. > > If minfx was extended to use constraints in BFGS, it should be quite > easy to make the Jacobian of the different relaxation dispersion > models, and implement those. > > That will speed up the analysis, and also make it possible to extract > the estimated errors from the Jacobian. > > But this is distant future. > > Best > Troels > > _______________________________________________ > 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
