Estimating statistical distributions using an integral identity.
We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114 (2005)]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method. The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function, and a joint distribution of amino acid backbone dihedral angles.
Applied Physics Program and Department of Bioengineering, Rice University, Houston, Texas 77005, USA.
Cheng
C
Zhang
Jianpeng
J
Ma
D000465:Algorithms; D000596:Amino Acids / Q000737:chemistry*; D006033:Glycylglycine / Q000737:chemistry; D016008:Statistical Distributions; D013816:Thermodynamics
D000596:Amino Acids; D006033:Glycylglycine