**From:** Dave Rogers (*wantye_at_gmail.com*)

**Date:** Wed Oct 15 2008 - 13:27:23 CDT

**Next message:**Meij, Henk: "RE: megatest test failure/MPI problem"**Previous message:**brmorgan_at_clarku.edu: "Using NAMD to calculate pair energy with many subset permutations"**In reply to:**Joshua Adelman: "Quantitative Test for Equilibration of Data Time Series"**Next in thread:**Peter Freddolino: "Re: Quantitative Test for Equilibration of Data Time Series"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

In stating that the system has reached equilibrium, there is a

fundamental assumption that the system dynamics does not have a

correlation time longer than the actual time observed (i.e. a

persistent long-time correlation). A first approach, as you suggest

is to "look" at the computed autocorrelation function for a quantity

of interest and make sure it approaches zero relatively rapidly. To

make this more quantitative you could fit to an exponential to get a

correlation time to compare to total sim. time.

Allen and Tildesley (Computer Simulation of Liquids) have a

discussion on using block averages of different sizes to estimate a

"statistical inefficiency" on pp.191-194 -- which is another way of

getting at the correlation time. Jaynes has a more abstract

discussion of time averages and ensemble averages on pp. 64-68 of

"Where Do We Stand on Maximum Entropy?"

(http://bayes.wustl.edu/etj/node1.html, no 36.) and in his book

Probability Theory, The Logic of Science, presents a Markov-chain

model for estimating correlations in dynamic processes which may be

worth further investigation.

There are also a host of advocates for re-doing everything several

times from random starting points in the literature. I am interested

in seeing what other answers come up for this question.

~ David Rogers

Dr. Thomas Beck Lab

University of Cincinnati

On Wed, Oct 15, 2008 at 1:06 PM, Joshua Adelman <jadelman_at_berkeley.edu> wrote:

*> Does anyone know of a quantitative test or analysis that can be applied to a
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*> data time series to test to see when the data has equilibrated? I have a
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*> large number of simulations that seem to be equilibrating on slightly
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*> different time scales and am trying to find an automated way of figuring out
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*> how much of the initial sampling needs to be discarded in order to calculate
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*> the average value of the time series. Most of the suggestions on this list
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*> seem to imply visual inspection of the data, which is sub-optimal for this
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*> application.
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*>
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*> Any suggestions would be appreciated.
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*>
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*> Josh
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*>
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*>
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*>
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*>
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