Hi Stephen,

computing errors from umbrella sampling is not trivial at al.

Generally, there are two possibilities:

- If each histogram overlaps only with one neighboring histogram, you *must* know the autocorrelation time of each window. This is often a problem in MD simulations, because there may be hidden slow transitions. In my experience, you always underestimate the autocorrelation time and as a consequence the statistical error. However, if you do know the autocorrelation time, then you can either (a) compute the PMF from blocks of the data (how you did), but this only works if the blocks are longer than the autocorrelation time or (b) use "g_wham -bs-method traj" to generate new "synthentic" histograms for bootstrapping (which incorporate the autocorrelation time). Important: You cannot do bootstrapping of complete histograms, because there is only one histogram at each window.

- If you have many histograms overlapping each other, or if you did umbrella sampling at each window multiple times, you can assume that the different histograms represent all possible histograms at the respective position of the reaction coordinate. Then, you can do bootstrapping of histograms with g_wham -bs-method b-hist. It is not obvious how many histograms you need at each position, but maybe 10 is a reasonable number.

Coming to your error from blocks of data (10-30, 30-50, 50-70, 70-100 ns). The small error you get could mean two things:
a) you have a well-converged PMF (good)
b) you have long autocorrelations. Therefore, the histograms from the blocks are similar. Therefore, you underestimate the error (bad).

So you see, it is not trivial to estimate errors from umbrella sampling. My experience is that bootstrapping of histograms is more reliable, but it requires that you have multiple histograms at each position (and these histograms should be uncorrelated!!). But at least, this way you do not need to know the autocorrelation times, but instead "only" need to generate histograms which are independent. The latter is easier in practice, because independent simulations are more likely to be uncorrelated than frames *within* one simulation.

I hope this helps a bit.

Cheers,
Jochen


Am 2/19/13 3:22 PM, schrieb Steven Neumann:
Dear Gmx Users,

I run 10 US windows of 100 ns each - ion binding protein. I have a
great convergence of profiles and good windows overlap.I tried to see
PMF profiles from 10-30, 30-50, 50-70, 70-100 ns and they look very
similar (Max. error would be 0.2 kcal/mol). The overal deltaG is about
-5 kcal/mol.

When I use g_wham with -nBootsrap 200 and -bins 200 I get error bars
of -1.2 kcal/mol which is very significant.
How can I impove my error bars? Why they are so large?

Steven


--
---------------------------------------------------
Dr. Jochen Hub
Computational Molecular Biophysics Group
Institute for Microbiology and Genetics
Georg-August-University of Göttingen
Justus-von-Liebig-Weg 11, 37077 Göttingen, Germany.
Phone: +49-551-39-14189
http://cmb.bio.uni-goettingen.de/
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