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These are all unpublished concepts though.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
Re: Diffusion Tensor - Global correlation time