[gmx-users] error estimates of free energy calculations

David van der Spoel spoel at xray.bmc.uu.se
Wed May 16 08:12:57 CEST 2007

Berk Hess wrote:
>> From: "David Mobley" <dmobley at gmail.com>
>> Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>> To: "Discussion list for GROMACS users" <gmx-users at gromacs.org>
>> Subject: Re: [gmx-users] error estimates of free energy calculations
>> Date: Tue, 15 May 2007 15:55:01 -0700
>> Jeroen,
>>> However, in my opinion (assuming the total error should be calculated
>>> from standard error propagation), the way g_analyze calculates the
>>> total error is incorrect. It results in an overestimation of this
>>> total error by at least a factor of sqrt((number of lambda points) -
>>> 1). This factor is 4.5 in my case, accounting for the larger part of
>>> my previoulsy mentioned loss of accuracy. And indeed, as you guys
>>> already mentioned, the remaining part may be explained from the fact
>>> that Berk uses twice as many lambda values.
>> Whoops! Justifies my paranoia about using other people's analysis
>> tools. :) The person responsible for the analysis tool should take a
>> look at this -- if the tool does error analysis for the integral, it
>> should do it properly.
> ah, g_analyze indeed seems to print an error estimate of the integral,
> I didn't know about this.
> But according to me this is totally wrong.
> It divides the sum of variances by n-1, whereas this should be n^2.
> I'll fix it for the next release.
It is the standard deviation, rigth? Which is what the source code says 
it is...

David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596,  	75124 Uppsala, Sweden
phone:	46 18 471 4205		fax: 46 18 511 755
spoel at xray.bmc.uu.se	spoel at gromacs.org   http://folding.bmc.uu.se

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