On Fri, 2006-10-06 at 03:29 +1000, Edward d'Auvergne wrote: > > I can add my observations, from spending much time hitting my head against > > these problems in a few different systems. I find that Lewis Kay's > > approach and Edward's new proposal (the 'full_analysis.py' approach) work > > well for differing systems. For very good data, both work well and > > converge on the same result. For data has a few 'outliers' (eg. residues > > affected by Rex or complex ns motions) Kay's approach can fail because > > the initial estimate of the diffusion constant is not good enough. On > > the other hand, Edward's approach seems more robust to these types > > outliers, but in my hands sometimes requires a very precise data set in > > order to converge. One clear benefit of Edward's approach is that > > failure is obvious - it simply doesn't converge on a diffusion ternsor, > > and chi2 eventually starts to rise as the tensor drifts into the wrong > > area. On the other hand, judging the success of the Kay approach can be > > much more difficult. > > That sounds pretty good! I can't complain about those observations :) > One thing I have to mention though, which is not at all obvious when > using my new approach, is that it is not the chi-squared value which > is optimised between iterations. It is actually something called the > Kullback-Liebler discrepancy, approximated by the AIC value, which is > optimised! The reason is because the mathematical model (the > diffusion tensor + all model-free models) is different between > iterations and hence comparing chi-squared values is meaningless. > These are all unpublished concepts though. In one paper which I have > submitted, I will show using real data that the chi-squared value > actually increases between iterations of 'full_analysis.py'. > Significantly the number of parameters decreases more than twice as > fast as the chi-squared value increases. Hence the AIC value > decreases between iterations (because AIC = chi2 + 2k, where k is the > number of parameters) while giving the false impression that something > wrong because the chi-squared value is increasing. If you use Grace > to plot chi2, k, and AIC all verses iteration number, the graphs will > show you exactly what is happening. >
Good point. I should have realised that. I've been making the mistake of judging convergence on chi2 alone, so perhaps I've been a bit hasty to ascribe failure in some cases. > > > In conclusion, my advice is to try both approaches on a carefully pruned > > dataset - it is well worth spending time on getting this right first up, > > because everything else depends on it. > > That is good advice. Comparing different results gives you a good > sense of what is real. The reduced spectral density mapping which is > built into relax is also very useful for comparison. Did you need to > use a pruned data set together with my new approach? Carefully > selected data is essential for obtaining a good initial estimate of > the diffusion tensor (for the application of Kay's paradigm - first > came the diffusion tensor). However this new approach is designed to > have absolutely every last bit of data thrown at it simultaneously. > It is designed to avoid the need for pruning. > I've tended to use pruned data sets because I've always had then around (beacuse I've tried Kay's approach). That said, I've generally found your approach is more robust to the outliers, but I've not tested it at all rigorously. Chris _______________________________________________ relax (http://nmr-relax.com) This is the relax-users 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-users
