[gmx-users] How to calculate the block averaging error from non-equilibrium MD simulations

[Justin A. Lemkul]

Yanmei Song wrote:
> Dear Justin:
> 
> Thank you so much for your quick response.
> 
> But I still don't get it. Should I calculate the standard error manually 
> by using the equations A17 (in B. Hess' s paper) after I get the result 
> by g_analyze. And then which value I should use for the sigma?
> 
> Here is the output :
> 
> invalid fit:  e.e. 15.6513  a 2.17585  tau1 28.9321  tau2 46.3966
> Will use a single exponential fit for set 1
> Set   1:  err.est. 21.0339  a 1  tau1 15.1648  tau2 0
> 
> I really appreciate your patience and help!
> 

When you use g_analyze -ee, you are trying to fit your data to equation A17. 
Your data cannot fit this expression (hence "invalid fit").  You may have 
convergence issues with your data or insufficient data to begin with, but I 
don't know much about that.  The single exponential fit given is (I believe) 
based on the last statement made in the paper:

"When the longest correlation time, tau2, is longer than the averaging interval 
and (1 - alpha)tau2 is not negligible compared to alpha*tau1, there is not 
enough statistics to estimate the error.  An example is given in Fig. 8."

An example of such a fit is shown in that figure.

-Justin

> 
> 
> On Fri, Nov 20, 2009 at 3:07 PM, Justin A. Lemkul <jalemkul at vt.edu 
> <mailto:jalemkul at vt.edu>> wrote:
> 
> 
> 
>     Yanmei Song wrote:
> 
>         Dear Justin:
> 
>         I really appreciate your response and help!
> 
>         I am confusing about the result by using this method. I found in
>         B. Hess's paper (Appendix, JCP, 116, 2002)  that " this gives a
>         standard error estimate for 1/eta of 29.5. "; and the error he
>         gives for that eta is 0.006. I thought the error should be
>         calculated as 1/29.5=0.034. Thank you again for your help!
> 
> 
>     The relationship is not a simple inversion as you've shown it.  That
>     is, (standard error of 1/eta) != 1/(standard error of eta).  The
>     standard error calculation depends on a number of factors, hence all
>     the math in the Appendix :)  An example is given in Fig. 8 of that
>     paper.
> 
>     -Justin
> 
> 
>     -- 
>     ========================================
> 
>     Justin A. Lemkul
>     Ph.D. Candidate
>     ICTAS Doctoral Scholar
>     Department of Biochemistry
>     Virginia Tech
>     Blacksburg, VA
>     jalemkul[at]vt.edu <http://vt.edu> | (540) 231-9080
>     http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin
> 
>     ========================================
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> 
> 
> 
> -- 
> Yanmei Song
> Ph.D. Candidate
> Department of Chemical Engineering
> Arizona State University

-- 
========================================

Justin A. Lemkul
Ph.D. Candidate
ICTAS Doctoral Scholar
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

========================================