Subject: [Q] Multiple histogram method

From: [email-masked]
Date: Fri, 12 Nov 1999 20:35:39 -0500 (EST)

Several works (e.g. [1, 2]) reporting multiple histogram techniques to
construct a free-energy surface, use a formulas containing a factor g,
which equals (1 + 2*tau), where \tau is referred to as the "integrated
correlation time".  The exact definition of tau is given in pp. 33-34
of [3], and amounts to the integral with respect to t from 0 to
infinity of <A(0)*A(t)> - <A>^2 divided by the variance of A, where A
is some quantity of interest.  I have tried to obtain numerically the
tau used in the multiple histogram techniques, but no matter how much
data I amass, I still end up with something that doesn't come even
close to converging (i.e. the integral above fluctuates widely
throughout as one lets the upper limit of integration grow to
infinity).

Does anybody know where I can find more info on how to compute this tau?

Thanks!

KJ

[1] Ferrenberg, A. M. and Swendsen, R. H. "Optimized Monte Carlo Data
Analysis", 1989, Phys. Rev. Lett. 63(12) 1195-1198.

[2] Kumar, S., et al. "The Weighted Histogram Analysis Method for
Free-Energy Calculations on Biomolecules.  I. The Method", 1992,
J. Comp. Chem., 13(8) 1011-1021.

[3] Binder, K. and Heermann, D. W. "Monte Carlo Simulation in
Statistical Physics", 2nd Corr. Ed., 1992, pp. 33-34.