[gmx-users] statistics of MD

[David van der Spoel]

On Tue, 2003-05-06 at 08:47, Evka Stefanekova wrote:
> Dear gmx users,
> 
> Maybe it's a trivial question, but I would like to know your opinions on 
> these topics: 
> 
> Let us have several simulations of the same system prepared. Each of them 
> has the same parameters, although slightly different initial conditions 
> (i.e. initial velocities of atoms are slightly different, also some atoms 
> may be slightly shifted). Let us also assume that the time of run of all 
> simulations is long enough for the studied phenomenon to finish. Is there 
> an argument from which we have that these simulations will result into 
> simillar final states? Isn't it necessary to run several simulations of 
> the same system and then statistically compute the most probable behavior 
> of the system? I mean, why we allways run just one simulation of some 
> system - how is this simulation statistically significant?

It depends on your system. If you have a simple liquid, all your runs
will converge to the same values. If you have a single protein in water
it will most likely not give the same statistics within the same time. 

The central limit theorem implies that a very long time average is the
same as an ensemble average. However the crux is "very long time".


-- 
Groeten, David.
________________________________________________________________________
Dr. David van der Spoel, 	Dept. of Cell & Mol. Biology
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://xray.bmc.uu.se/~spoel
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++