Re: statistical error of mean force in (NAMD) ABF calculations

From: Jeff Comer (
Date: Thu Jul 02 2015 - 09:09:38 CDT


I did the statistical error calculations for the paper you mentioned, and
I'd like to put together a simple script for it. However, a major barrier
for calculating the uncertainty in an automated way is determining the
autocorrelation time (τ in equation 24), which requires a lot of statistics
and is fairly sensitive to exactly how you define it. Furthermore, this
autocorrelation time requires information not available in the .grad and
.count files (you need .colvars.traj with a fairly low
"colvarsTrajFrequency"). The variance of the force (<ΔF^2>) also cannot be
calculated from the .grad and .count files. It requires statistics of the
system force, for which you need "outputSystemForce" in your colvars

In my opinion, the best way to estimate the statistical uncertainty remains
doing a few independent runs.

Also, note that in the paper we show that <ΔF^2> and the autocorrelation
time typically do not depend a lot on the details of the system, barring a
major inhomogeneity like a water–vacuum interface. I've even found that
<ΔF^2> varies little between a water molecule in water or in the center of
a lipid bilayer. Thus, you can probably do a few exemplary calculations to
pin down <ΔF^2> and τ, and then use equation 24 for similar systems
(perhaps different windows on the same collective variable) treating <ΔF^2>
and τ constant and allowing only n (from the .count file) to vary. This is
probably the most efficient way to estimate the statistical uncertainty if
doing independent runs is infeasible. Unfortunately, none of these
approaches really lend themselves to a blackbox treatment.


Jeffrey Comer, PhD
Assistant Professor
Institute of Computational Comparative Medicine
Nanotechnology Innovation Center of Kansas State
Kansas State University
Office: P-213 Mosier Hall
Phone: 785-532-6311

On Wed, Jul 1, 2015 at 5:09 AM, Branko <> wrote:

> Dear ABF developers,
> In J. Phys. Chem. B 2015, 119, 1129 it is described how statistical error
> of mean force in ABF could be calculated. Using two colvars make the whole
> calculation something more complicated. Just as an idea, maybe some script
> could be included in future releases which can be used to calculate
> statistical error of mean force; probably from the ABF output files (.grad
> and .count)
> Branko

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